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Publications of Samit Dasgupta    :chronological  alphabetical  combined listing:

%% Papers Published   
@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 = {© 2018 American Mathematical Society. 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 = {© European Mathematical Society 2018. 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{fds339636,
   Author = {Samit Dasgupta, and Mahesh Kakde, and Kevin Ventullo},
   Title = {On the Gross–Stark Conjecture},
   Journal = {Annals of Mathematics},
   Volume = {188},
   Number = {3},
   Pages = {833-833},
   Publisher = {Annals of Mathematics, Princeton U},
   Year = {2018},
   url = {http://dx.doi.org/10.4007/annals.2018.188.3.3},
   Abstract = {© 2018 Department of Mathematics, Princeton University. 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{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 = {© 2016, Fondation Carl-Herz and Springer International
             Publishing Switzerland. 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 = {© 2015, Springer-Verlag Berlin Heidelberg. 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 = {January},
   url = {http://dx.doi.org/10.1112/S0010437X1400788X},
   Abstract = {© Foundation Compositio Mathematica 2015. 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 GL<inf>n</inf>,
             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 = {© Swiss Mathematical Society. We define a cocycle on
             GL<inf>n</inf>(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 = {© Cambridge University Press 2014. 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{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 = {July},
   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 = {July},
   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 = {a 1 ,..., a k } and B = {b 1 ,..., b k } be two
             subsets of an Abelian group G, k ≤ |G|. Snevily
             conjectured that, when G is of odd order, there is a
             permutation π ≤ S k such that the sums a i + b π(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 (Z p ) α and Z pα 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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