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Publications of Samit Dasgupta    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds359781,
   Author = {Dasgupta, S and Kakde, M},
   Title = {On constant terms of Eisenstein series},
   Journal = {Acta Arithmetica},
   Volume = {200},
   Number = {2},
   Pages = {119-147},
   Year = {2021},
   Month = {January},
   url = {http://dx.doi.org/10.4064/aa200621-24-2},
   Doi = {10.4064/aa200621-24-2},
   Key = {fds359781}
}

@article{fds345674,
   Author = {Dasgupta, S and Spiess, M},
   Title = {On the characteristic polynomial of the gross regulator
             matrix},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {372},
   Number = {2},
   Pages = {803-827},
   Year = {2019},
   Month = {January},
   url = {http://dx.doi.org/10.1090/tran/7393},
   Abstract = {We present a conjectural formula for the principal minors
             and the characteristic polynomial of Gross’s regulator
             matrix associated to a totally odd character of a totally
             real field. The formula is given in terms of the Eisenstein
             cocycle, which was defined and studied earlier by the
             authors and collaborators. For the determinant of the
             regulator matrix, our conjecture follows from recent work of
             Kakde, Ventullo, and the first author. For the diagonal
             entries, our conjecture overlaps with the conjectural
             formula presented in our prior work. The intermediate cases
             are new and provide a refinement of the Gross-Stark
             conjecture.},
   Doi = {10.1090/tran/7393},
   Key = {fds345674}
}

@article{fds339636,
   Author = {Dasgupta, S and Kakde, M and Ventullo, K},
   Title = {On the Gross-Stark Conjecture},
   Journal = {Annals of Mathematics},
   Volume = {188},
   Number = {3},
   Pages = {833-870},
   Publisher = {Annals of Mathematics, Princeton U},
   Year = {2018},
   Month = {November},
   url = {http://dx.doi.org/10.4007/annals.2018.188.3.3},
   Abstract = {In 1980, Gross conjectured a formula for the expected
             leading term at s=0 of the Deligne-Ribet p-adic L-function
             associated to a totally even character ϕ of a totally real
             field F. The conjecture states that after scaling by
             L(ϕω-1,0), this value is equal to a p-adic regulator of
             units in the abelian extension of F cut out by ϕω-1. In
             this paper, we prove Gross's conjecture.},
   Doi = {10.4007/annals.2018.188.3.3},
   Key = {fds339636}
}

@article{fds338508,
   Author = {Dasgupta, S and Voight, J},
   Title = {Sylvester’s problem and mock heegner points},
   Journal = {Proceedings of the American Mathematical
             Society},
   Volume = {146},
   Number = {8},
   Pages = {3257-3273},
   Publisher = {American Mathematical Society (AMS)},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1090/proc/14008},
   Abstract = {We prove that if p ≡ 4, 7 (mod 9) is prime and 3 is not a
             cube modulo p, then both of the equations x3 + y3 = p and x3
             + y3 = p2 have a solution with x, y ∈ ℚ.},
   Doi = {10.1090/proc/14008},
   Key = {fds338508}
}

@article{fds339289,
   Author = {Dasgupta, S and Spieß, M},
   Title = {Partial zeta values, Gross's tower of fields conjecture, and
             Gross-Stark units},
   Journal = {Journal of the European Mathematical Society},
   Volume = {20},
   Number = {11},
   Pages = {2643-2683},
   Publisher = {European Mathematical Publishing House},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.4171/JEMS/821},
   Abstract = {We prove a conjecture of Gross regarding the “order of
             vanishing” of Stickelberger elements relative to an
             abelian tower of fields and give a cohomological
             construction of the conjectural Gross-Stark units. This is
             achieved by introducing an integral version of the
             Eisenstein cocycle.},
   Doi = {10.4171/JEMS/821},
   Key = {fds339289}
}

@article{fds338509,
   Author = {Dasgupta, S and Spieß, M},
   Title = {The Eisenstein cocycle and Gross’s tower of fields
             conjecture},
   Journal = {Annales Mathématiques Du Québec},
   Volume = {40},
   Number = {2},
   Pages = {355-376},
   Publisher = {Springer Nature},
   Year = {2016},
   Month = {August},
   url = {http://dx.doi.org/10.1007/s40316-015-0046-2},
   Abstract = {This paper is an announcement of the following result, whose
             proof will be forthcoming. Let F be a totally real number
             field, and let F⊂ K⊂ L be a tower of fields with L / F
             a finite abelian extension. Let I denote the kernel of the
             natural projection from Z[ Gal (L/ F) ] to Z[ Gal (K/ F) ].
             Let Θ ∈ Z[ Gal (L/ F) ] denote the Stickelberger element
             encoding the special values at zero of the partial zeta
             functions of L / F, taken relative to sets S and T in the
             usual way. Let r denote the number of places in S that split
             completely in K. We show that Θ ∈ Ir, unless K is totally
             real in which case we obtain Θ ∈ Ir-1 and 2 Θ ∈ Ir.
             This proves a conjecture of Gross up to the factor of 2 in
             the case that K is totally real and # S≠ r. In this
             article we sketch the proof in the case that K is totally
             complex.},
   Doi = {10.1007/s40316-015-0046-2},
   Key = {fds338509}
}

@article{fds338510,
   Author = {Dasgupta, S},
   Title = {Factorization of p-adic Rankin L-series},
   Journal = {Inventiones Mathematicae},
   Volume = {205},
   Number = {1},
   Pages = {221-268},
   Publisher = {Springer Nature},
   Year = {2016},
   Month = {July},
   url = {http://dx.doi.org/10.1007/s00222-015-0634-4},
   Abstract = {We prove that the p-adic L-series of the tensor square of a
             p-ordinary modular form factors as the product of the
             symmetric square p-adic L-series of the form and a
             Kubota–Leopoldt p-adic L-series. This establishes a
             generalization of a conjecture of Citro. Greenberg’s
             exceptional zero conjecture for the adjoint follows as a
             corollary of our theorem. Our method of proof follows that
             of Gross, who proved a factorization result for the Katz
             p-adic L-series associated to the restriction of a Dirichlet
             character. Whereas Gross’s method is based on comparing
             circular units with elliptic units, our method is based on
             comparing these same circular units with a new family of
             units (called Beilinson–Flach units) that we construct.
             The Beilinson–Flach units are constructed using Bloch’s
             intersection theory of higher Chow groups applied to
             products of modular curves. We relate these units to special
             values of classical and p-adic L-functions using work of
             Beilinson (as generalized by Lei–Loeffler–Zerbes) in the
             archimedean case and Bertolini–Darmon–Rotger (as
             generalized by Kings–Loeffler–Zerbes) in the p-adic
             case. Central to our method are two compatibility theorems
             regarding Bloch’s intersection pairing and the classical
             and p-adic Beilinson regulators defined on higher Chow
             groups.},
   Doi = {10.1007/s00222-015-0634-4},
   Key = {fds338510}
}

@article{fds338511,
   Author = {Bellaïche, J and Dasgupta, S},
   Title = {The p-adic L-functions of evil Eisenstein
             series},
   Journal = {Compositio Mathematica},
   Volume = {151},
   Number = {6},
   Pages = {999-1040},
   Publisher = {Oxford University Press (OUP)},
   Year = {2015},
   Month = {June},
   url = {http://dx.doi.org/10.1112/S0010437X1400788X},
   Abstract = {We compute the p-adic L-functions of evil Eisenstein series,
             showing that they factor as products of two Kubota-Leopoldt
             p-adic L-functions times a logarithmic term. This proves in
             particular a conjecture of Glenn Stevens.},
   Doi = {10.1112/S0010437X1400788X},
   Key = {fds338511}
}

@article{fds338512,
   Author = {Charollois, P and Dasgupta, S and Greenberg, M},
   Title = {Integral Eisenstein cocycles on GLn, II:
             Shintani's method},
   Journal = {Commentarii Mathematici Helvetici},
   Volume = {90},
   Number = {2},
   Pages = {435-477},
   Publisher = {European Mathematical Publishing House},
   Year = {2015},
   Month = {January},
   url = {http://dx.doi.org/10.4171/CMH/360},
   Abstract = {We define a cocycle on GLn(Q) using Shintani's method. This
             construction is closely related to earlier work of Solomon
             and Hill, but differs in that the cocycle property is
             achieved through the introduction of an auxiliary
             perturbation vector Q. As a corollary of our result we
             obtain a new proof of a theorem of Diaz y Diaz and Friedman
             on signed fundamental domains, and give a cohomological
             reformulation of Shintani's proof of the Klingen-Siegel
             rationality theorem on partial zeta functions of totally
             real fields. Next we relate the Shintani cocycle to the
             Sczech cocycle by showing that the two differ by the sum of
             an explicit coboundary and a simple "polar" cocycle. This
             generalizes a result of Sczech and Solomon in the case n =
             2. Finally, we introduce an integral version of our cocycle
             by smoothing at an auxiliary prime l. This integral
             refinement has strong arithmetic consequences. We showed in
             previous work that certain specializations of the smoothed
             class yield the p-adic L-functions of totally real fields.
             Furthermore, combining our cohomological construction with a
             theorem of Spiess, one deduces that that the order of
             vanishing of these p-adic L-functions is at least as large
             as the expected one.},
   Doi = {10.4171/CMH/360},
   Key = {fds338512}
}

@article{fds338513,
   Author = {Bertolini, M and Castella, F and Darmon, H and Dasgupta, S and Prasanna,
             K and Rotger, V},
   Title = {P-adic L-functions and Euler systems: A tale in two
             trilogies},
   Pages = {52-101},
   Booktitle = {Automorphic Forms and Galois Representations:
             volume1},
   Year = {2014},
   Month = {January},
   ISBN = {9781107691926},
   url = {http://dx.doi.org/10.1007/9781107446335.004},
   Abstract = {This chapter surveys six different special value formulae
             for p-adic L-functions, stressing their common features and
             their eventual arithmetic applications via Kolyvagin’s
             theory of “Euler systems”, in the spirit of Coates-Wiles
             and Kato-Perrin-Riou.},
   Doi = {10.1007/9781107446335.004},
   Key = {fds338513}
}

@article{fds353876,
   Author = {Charollois, P and Dasgupta, S},
   Title = {Integral Eisenstein cocycles on $\mathbf{GL}_n$, I:
             Sczech’s cocycle and $p$-adic $L$-functions of totally
             real fields},
   Journal = {Cambridge Journal of Mathematics},
   Volume = {2},
   Number = {1},
   Pages = {49-90},
   Publisher = {International Press of Boston},
   Year = {2014},
   url = {http://dx.doi.org/10.4310/cjm.2014.v2.n1.a2},
   Doi = {10.4310/cjm.2014.v2.n1.a2},
   Key = {fds353876}
}

@article{fds338514,
   Author = {Dasgupta, S},
   Title = {A conjectural product formula for Brumer-Stark units over
             real quadratic fields},
   Journal = {Journal of Number Theory},
   Volume = {133},
   Number = {3},
   Pages = {915-925},
   Publisher = {Elsevier BV},
   Year = {2013},
   Month = {March},
   url = {http://dx.doi.org/10.1016/j.jnt.2012.02.013},
   Abstract = {Following methods of Hayes, we state a conjectural product
             formula for ratios of Brumer-Stark units over real quadratic
             fields. © 2012 Elsevier Inc.},
   Doi = {10.1016/j.jnt.2012.02.013},
   Key = {fds338514}
}

@article{fds338515,
   Author = {Dasgupta, S and Greenberg, M},
   Title = {ℒ-invariants and Shimura curves},
   Journal = {Algebra & Number Theory},
   Volume = {6},
   Number = {3},
   Pages = {455-485},
   Publisher = {Mathematical Sciences Publishers},
   Year = {2012},
   Month = {July},
   url = {http://dx.doi.org/10.2140/ant.2012.6.455},
   Abstract = {In earlier work, the second named author described how to
             extract Darmon-style ℒ-invariants from modular forms on
             Shimura curves that are special at p. In this paper, we show
             that these ℒ-invariants are preserved by the
             Jacquet-Langlands correspondence. As a consequence, we prove
             the second named author's period conjecture in the case
             where the base field is ℚ. As a further application of our
             methods, we use integrals of Hida families to describe
             Stark-Heegner points in terms of a certain Abel-Jacobi map.
             ©2012 by Mathematical Sciences Publishers.},
   Doi = {10.2140/ant.2012.6.455},
   Key = {fds338515}
}

@article{fds338516,
   Author = {Dasgupta, S and Darmon, H and Pollack, R},
   Title = {Hilbert modular forms and the Gross-Stark
             conjecture},
   Journal = {Annals of Mathematics},
   Volume = {174},
   Number = {1},
   Pages = {439-484},
   Publisher = {Annals of Mathematics, Princeton U},
   Year = {2011},
   Month = {January},
   url = {http://dx.doi.org/10.4007/annals.2011.174.1.12},
   Abstract = {Let F be a totally real field and χ an abelian totally odd
             character of F. In 1988, Gross stated a p-adic analogue of
             Stark's conjecture that relates the value of the derivative
             of the p-adic L-function associated to χ and the p-adic
             logarithm of a p-unit in the extension of F cut out by χ.
             In this paper we prove Gross's conjecture when F is a real
             quadratic field and χ is a narrow ring class character. The
             main result also applies to general totally real fields for
             which Leopoldt's conjecture holds, assuming that either
             there are at least two primes above p in F, or that a
             certain condition relating the L-invariants of χ and χ-1
             holds. This condition on L-invariants is always satisfied
             when χ is quadratic.},
   Doi = {10.4007/annals.2011.174.1.12},
   Key = {fds338516}
}

@article{fds338517,
   Author = {Dasgupta, S and Miller, A},
   Title = {A Shintani-type formula for Gross-Stark units over function
             fields},
   Journal = {Journal of Mathematical Sciences},
   Volume = {16},
   Number = {3},
   Pages = {415-440},
   Year = {2009},
   Month = {December},
   Abstract = {Let F be a totally real number field of degree n, and let H
             be a finite abelian extension of F. Let p denote a prime
             ideal of F that splits completely in H. Following Brumer and
             Stark, Tate conjectured the existence of a p-unit u in H
             whose p-adic absolute values are related in a precise way to
             the partial zeta-functions of the extension H/F. Gross later
             refined this conjecture by proposing a formula for the
             p-adic norm of the element u. Recently, using methods of
             Shintani, the first author refined the conjecture further by
             proposing an exact formula for u in the p-adic completion of
             H. In this article we state and prove a function field
             analogue of this Shintani-type formula. The role of the
             totally real field F is played by the function field of a
             curve over a finite field in which n places have been
             removed. These places represent the "real places" of F. Our
             method of proof follows that of Hayes, who proved Gross's
             conjecture for function fields using the theory of Drinfeld
             modules and their associated exponential
             functions.},
   Key = {fds338517}
}

@article{fds338518,
   Author = {Dasgupta, S},
   Title = {Shintani zeta functions and gross-stark units for totally
             real fields},
   Journal = {Duke Mathematical Journal},
   Volume = {143},
   Number = {2},
   Pages = {225-279},
   Publisher = {Duke University Press},
   Year = {2008},
   Month = {June},
   url = {http://dx.doi.org/10.1215/00127094-2008-019},
   Abstract = {Let F be a totally real number field, and let p be a finite
             prime of F such that p splits completely in the finite
             abelian extension H of F. Tate has proposed a conjecture
             [22, Conjecture 5.4] stating the existence of a p-unit u in
             H with absolute values at the places above p specified in
             terms of the values at zero of the partial zeta functions
             associated to H/F. This conjecture is an analogue of Stark's
             conjecture, which Tate called the Brumer-Stark conjecture.
             Gross [12, Conjecture 7.6] proposed a refinement of the
             Brumer-Stark conjecture that gives a conjectural formula for
             the image of u in Fpx/Ê, where FP denotes the completion of
             F at p and Ê denotes the topological closure of the group
             of totally positive units E of F. We present a further
             refinement of Gross's conjecture by proposing a conjectural
             formula for the exact value of u in Fpx.},
   Doi = {10.1215/00127094-2008-019},
   Key = {fds338518}
}

@article{fds338519,
   Author = {Dasgupta, S},
   Title = {Computations of elliptic units for real quadratic
             fields},
   Journal = {Canadian Journal of Mathematics},
   Volume = {59},
   Number = {3},
   Pages = {553-574},
   Publisher = {Canadian Mathematical Society},
   Year = {2007},
   Month = {January},
   url = {http://dx.doi.org/10.4153/CJM-2007-023-0},
   Abstract = {Let K be a real quadratic field, and p a rational prime
             which is inert in K. Let a be a modular unit on Γ0(N). In
             an earlier joint article with Henri Darmon, we presented the
             definition of an element u(α, τ) ε Kpx attached to a and
             each τ ε K. We conjectured that the p-adic number u(α,
             τ) lies in a specific ring class extension of K depending
             on τ, and proposed a "Shimura reciprocity law" describing
             the permutation action of Galois on the set of u(α, τ),
             This article provides computational evidence for these
             conjectures. We present an efficient algorithm for computing
             u(α, τ), and implement this algorithm with the modular
             unit α(z) = Δ(z) 2 Δ(4z)3,Δ(2z)3. Using p = 3, 5, 7, and
             11, and all real quadratic fields K with discriminant D <
             500 such that 2 splits in K and K contains no unit of
             negative norm, we obtain results supporting our conjectures.
             One of the theoretical results in this paper is that a
             certain measure used to define w(α, τ) is shown to be
             Z-valued rather than only Zp ∩ Q-valued; this is an
             improvement over our previous result and allows for a
             precise definition of u(α, τ), instead of only up to a
             root of unity. © Canadian Mathematical Society
             2007.},
   Doi = {10.4153/CJM-2007-023-0},
   Key = {fds338519}
}

@article{fds338520,
   Author = {Darmon, H and Dasgupta, S},
   Title = {Elliptic units for real quadratic fields},
   Journal = {Annals of Mathematics},
   Volume = {163},
   Number = {1},
   Pages = {301-346},
   Publisher = {Annals of Mathematics, Princeton U},
   Year = {2006},
   Month = {January},
   url = {http://dx.doi.org/10.4007/annals.2006.163.301},
   Doi = {10.4007/annals.2006.163.301},
   Key = {fds338520}
}

@article{fds338521,
   Author = {Dasgupta, S},
   Title = {Stark-Heegner points on modular Jacobians},
   Journal = {Annales Scientifiques De L’École Normale
             Supérieure},
   Volume = {38},
   Number = {3},
   Pages = {427-469},
   Publisher = {Societe Mathematique de France},
   Year = {2005},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.ansens.2005.03.002},
   Abstract = {We present a construction which lifts Darmon's Stark-Heegner
             points from elliptic curves to certain modular Jacobians.
             Let N be a positive integer and let p be a prime not
             dividing N. Our essential idea is to replace the modular
             symbol attached to an elliptic curve E of conductor Np with
             the universal modular symbol for Γ0(Np). We then construct
             a certain torus T over Qp and lattice L ⊂ T, and prove
             that the quotient T/L is isogenous to the maximal toric
             quotient J0(Np)p-new of the Jacobian of X0(Np). This theorem
             generalizes a conjecture of Mazur, Tate, and Teitelbaum on
             the p-adic periods of elliptic curves, which was proven by
             Greenberg and Stevens. As a by-product of our theorem, we
             obtain an efficient method of calculating the p-adic periods
             of J0(Np)p-new. © 2005 Elsevier SAS. All rights
             reserved.},
   Doi = {10.1016/j.ansens.2005.03.002},
   Key = {fds338521}
}

@article{fds338523,
   Author = {Biss, DK and Dasgupta, S},
   Title = {A presentation for the unipotent group over rings with
             identity},
   Journal = {Journal of Algebra},
   Volume = {237},
   Number = {2},
   Pages = {691-707},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {March},
   url = {http://dx.doi.org/10.1006/jabr.2000.8604},
   Abstract = {For a ring R with identity, define Unipn(R) to be the group
             of upper-triangular matrices over R all of whose diagonal
             entries are 1. For i = 1,2,...,n - 1, let Si denote the
             matrix whose only nonzero off-diagonal entry is a 1 in the
             ith row and (i + 1)st column. Then for any integer m
             (including m = 0), it is easy to see that the Si generate
             Unipn(Z/mZ). Reiner gave relations among the Si which he
             conjectured gave a presentation for Unipn(Z/2Z). This
             conjecture was proven by Biss [Comm. Algebra26 (1998),
             2971-2975] and an analogous conjecture was made for
             Unipn(Z/mZ) in general. We prove this conjecture, as well as
             a generalization of the conjecture to unipotent groups over
             arbitrary rings. © 2001 Academic Press.},
   Doi = {10.1006/jabr.2000.8604},
   Key = {fds338523}
}

@article{fds338522,
   Author = {Dasgupta, S and Károlyi, G and Serra, O and Szegedy,
             B},
   Title = {Transversals of additive Latin squares},
   Journal = {Israel Journal of Mathematics},
   Volume = {126},
   Number = {1},
   Pages = {17-28},
   Publisher = {Springer Nature},
   Year = {2001},
   Month = {January},
   url = {http://dx.doi.org/10.1007/BF02784149},
   Abstract = {Let A = {a1,..., ak} and B = {b1,..., bk} be two subsets of
             an Abelian group G, k ≤ |G|. Snevily conjectured that,
             when G is of odd order, there is a permutation π ≤ Sk
             such that the sums ai + bπ(i), 1 ≤ i ≤ k, are pairwise
             different. Alon showed that the conjecture is true for
             groups of prime order, even when A is a sequence of k < |G|
             elements, i.e., by allowing repeated elements in A. In this
             last sense the result does not hold for other Abelian
             groups. With a new kind of application of the polynomial
             method in various finite and infinite fields we extend
             Alon's result to the groups (Zp)α and Zpα in the case k <
             p, and verify Snevily's conjecture for every cyclic group of
             odd order.},
   Doi = {10.1007/BF02784149},
   Key = {fds338522}
}

@article{fds338524,
   Author = {Dasgupta, S},
   Title = {On the size of minimum super arrovian domains},
   Journal = {Siam Journal on Discrete Mathematics},
   Volume = {12},
   Number = {4},
   Pages = {524-534},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1999},
   Month = {January},
   url = {http://dx.doi.org/10.1137/S0895480198332521},
   Abstract = {Arrow's celebrated impossibility theorem states that a
             sufficiently diverse domain of voter preference profiles
             cannot be mapped into social orders of the alternatives
             without violating at least one of three appealing
             conditions. Following Fishburn and Kelly, we define a set of
             strict preference profiles to be super Arrovian if Arrow's
             impossibility theorem holds for this set and each of its
             strict preference profile supersets. We write σ(m, n) for
             the size of the smallest super Arrovian set for m
             alternatives and n voters. We show that σ(m, 2) = [2m/m-2]
             and σ(3, 3) = 19. We also show that σ(m, n) is bounded by
             a constant for fixed n and bounded on both sides by a
             constant times 2n for fixed m. In particular, we find that
             limn→∞ σ(3, n)/2n = 3. Finally, we answer two questions
             posed by Fishburn and Kelly on the structure of minimum and
             minimal super Arrovian sets.},
   Doi = {10.1137/S0895480198332521},
   Key = {fds338524}
}

 

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