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Publications of Heekyoung Hahn    :chronological  alphabetical  combined listing:

%% Books   
@book{fds320419,
   Author = {Berndt, BC},
   Title = {Ramanujan's Forty Identities for the Rogers-Ramanujan
             Functions},
   Volume = {188},
   Number = {880},
   Pages = {96 pages},
   Booktitle = {Mem. Amer. Math. Soc},
   Publisher = {American Mathematical Soc.},
   Year = {2007},
   ISBN = {082183973X},
   Abstract = {When seeking proofs of Ramanujan's identities for the
             Rogers–Ramanujan functions, Watson, i.e., G. N. Watson,
             was not an “idiot.” He, L. J. ... functions. In this
             paper, for 35 of the 40 identities, we offer proofs that are
             in the spirit of Ramanujan.},
   Key = {fds320419}
}


%% Papers Published   
@article{fds354996,
   Author = {Hahn, H},
   Title = {Poles of triple product L-functions involving monomial
             representations},
   Journal = {International Journal of Number Theory},
   Volume = {17},
   Number = {2},
   Pages = {479-486},
   Year = {2021},
   Month = {March},
   url = {http://dx.doi.org/10.1142/S1793042120400291},
   Abstract = {In this paper, we study the order of the pole of the triple
             tensor product L-functions L(s,π1 × π2 × π3,⊗3) for
             cuspidal automorphic representations πi of GLni(F) in the
             setting where one of the πi is a monomial representation.
             In the view of Brauer theory, this is a natural setting to
             consider. The results provided in this paper give crucial
             examples that can be used as a point of reference for
             Langlands' beyond endoscopy proposal.},
   Doi = {10.1142/S1793042120400291},
   Key = {fds354996}
}

@article{fds320417,
   Author = {Hahn, H},
   Title = {On Classical groups detected by the triple tensor product
             and the Littlewood–Richardson semigroup},
   Journal = {Research in Number Theory},
   Volume = {2},
   Number = {1},
   Pages = {1-12},
   Publisher = {Springer Nature},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1007/s40993-016-0049-3},
   Abstract = {Langlands’ beyond endoscopy proposal for establishing
             functoriality motivates the study of irreducible subgroups
             of GL that stabilize a line in a given repesentation of GL .
             Such subgroups are said to be detected by the
             representation. In this paper we continue our study of the
             important special case where the representation of GL is the
             triple tensor product representation ⊗ . We prove a family
             of results describing when subgroups isomorphic to classical
             groups of type B , C , D are detected. n n n n n 2 n
             3},
   Doi = {10.1007/s40993-016-0049-3},
   Key = {fds320417}
}

@article{fds320109,
   Author = {Hahn, H},
   Title = {On tensor third L-functions of automorphic representations
             of GLn(AF)},
   Journal = {Proceedings of the American Mathematical
             Society},
   Volume = {144},
   Number = {12},
   Pages = {5061-5069},
   Publisher = {American Mathematical Society (AMS)},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1090/proc/13134},
   Abstract = {Langlands’ beyond endoscopy proposal for establishing
             functoriality motivates interesting and concrete problems in
             the representation theory of algebraic groups. We study
             these problems in a setting related to the Langlands
             L-functions L(s, π, ⊗ ), where π is a cuspidal
             automorphic representation of GL (A )and F is a global
             field. 3 n F},
   Doi = {10.1090/proc/13134},
   Key = {fds320109}
}

@article{fds302444,
   Author = {Getz, JR and Hahn, H},
   Title = {A general simple relative trace formula},
   Journal = {Pacific Journal of Mathematics},
   Volume = {277},
   Number = {1},
   Pages = {99-118},
   Publisher = {Mathematical Sciences Publishers},
   Year = {2015},
   Month = {January},
   ISSN = {0030-8730},
   url = {http://dx.doi.org/10.2140/pjm.2015.277.99},
   Abstract = {In this paper we prove a relative trace formula for all
             pairs of connected algebraic groups H ≤ G × G, with G a
             reductive group and H the direct product of a reductive
             group and a unipotent group, given that the test function
             satisfies simplifying hypotheses. As an application, we
             prove a relative analogue of the Weyl law, giving an
             asymptotic formula for the number of eigenfunctions of the
             Laplacian on a locally symmetric space associated to G
             weighted by their L<sup>2</sup>-restriction norm over a
             locally symmetric subspace associated to H<inf>0</inf> ≤
             G.},
   Doi = {10.2140/pjm.2015.277.99},
   Key = {fds302444}
}

@article{fds320418,
   Author = {Hahn, H and Akhtari, S and David, C and Thompson,
             L},
   Title = {Distribution of square-free values of sequences associated
             with elliptic curves},
   Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
             Later},
   Volume = {606},
   Pages = {171-188},
   Publisher = {American Mathematical Society},
   Address = {Providence, RI},
   Year = {2013},
   Month = {October},
   Key = {fds320418}
}

@article{fds243559,
   Author = {Getz, JR and Hahn, H},
   Title = {ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR
             VARIETIES},
   Journal = {International Journal of Number Theory},
   Volume = {10},
   Number = {2},
   Pages = {1-16},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2013},
   ISSN = {1793-0421},
   url = {http://dx.doi.org/10.1142/s1793042113500875},
   Abstract = {Let E/ be a totally real number field that is Galois over ,
             and let be a cuspidal, nondihedral automorphic
             representation of GL2(E) that is in the lowest weight
             discrete series at every real place of E. The representation
             cuts out a motive Mét(π∞) from the ℓ-adic middle
             degree intersection cohomology of an appropriate Hilbert
             modular variety. If ℓ is sufficiently large in a sense
             that depends on π we compute the dimension of the space of
             Tate classes in M ét(π∞). Moreover if the space of Tate
             classes on this motive over all finite abelian extensions
             k/E is at most of rank one as a Hecke module, we prove that
             the space of Tate classes in M ét(π∞) is spanned by
             algebraic cycles. © 2014 World Scientific Publishing
             Company.},
   Doi = {10.1142/s1793042113500875},
   Key = {fds243559}
}

@article{fds243560,
   Author = {Hahn, H},
   Title = {A simple twisted relative trace formula},
   Journal = {International Mathematics Research Notices},
   Volume = {2009},
   Number = {21},
   Pages = {3957-3978},
   Publisher = {Oxford University Press (OUP)},
   Year = {2009},
   Month = {December},
   url = {http://dx.doi.org/10.1093/imrn/rnp075},
   Abstract = {In this article we derive a simple twisted relative trace
             formula. © 2009 The Author. Published by Oxford University
             Press. All rights reserved.},
   Doi = {10.1093/imrn/rnp075},
   Key = {fds243560}
}

@article{fds243561,
   Author = {Hahn, H},
   Title = {Eisenstein series associated with Γ0(2)},
   Journal = {Ramanujan Journal},
   Volume = {15},
   Number = {2},
   Pages = {235-257},
   Year = {2008},
   Month = {February},
   url = {http://dx.doi.org/10.1007/s11139-007-9075-z},
   Abstract = {In this paper, we define the normalized Eisenstein series P,
             e, and Q associated with Γ (2), and derive three
             differential equations satisfied by them from some
             trigonometric identities. By using these three formulas, we
             define a differential equation depending on the weights of
             modular forms on Γ (2) and then construct its modular
             solutions by using orthogonal polynomials and Gaussian
             hypergeometric series. We also construct a certain class of
             infinite series connected with the triangular numbers.
             Finally, we derive a combinatorial identity from a formula
             involving the triangular numbers. © 2008 Springer
             Science+Business Media, LLC. 0 0},
   Doi = {10.1007/s11139-007-9075-z},
   Key = {fds243561}
}

@article{fds302442,
   Author = {Hahn, H},
   Title = {Convolution sums of some functions on divisors},
   Journal = {Rocky Mountain Journal of Mathematics},
   Volume = {37},
   Number = {5},
   Pages = {1593-1622},
   Publisher = {Rocky Mountain Mathematics Consortium},
   Year = {2007},
   Month = {December},
   ISSN = {0035-7596},
   url = {http://dx.doi.org/10.1216/rmjm/1194275937},
   Abstract = {One of the main goals in this paper is to establish
             convolution sums of functions for the divisor sums σ̃ (n)
             = Σ (-1) d and σ̂ = Σ (-l) d , for certain s, which were
             first defined by Glaisher. We first introduce three
             functions P(q), E(q), and Q(q) related to σ̃(n), σ̂(n),
             and σ̃ (n), respectively, and then we evaluate them in
             terms of two parameters x and z in Ramanujan's theory of
             elliptic functions. Using these formulas, we derive some
             identities from which we can deduce convolution sum
             identities. We discuss some formulae for determining r (n)
             and r (n), s = 4, 8, in terms of σ̃(n), σ̂(n), and σ̃
             (n), where r (n) denotes the number of representations of n
             as a sum of s squares and δ (n) denotes the number of
             representations of n as a sum of s triangular numbers.
             Finally, we find some partition congruences by using the
             notion of colored partitions. Copyright ©2007 Rocky
             Mountain Mathematics Consortium. s d/n s d/n 3 s s 3 s s d-1
             s (n/d)-1 s},
   Doi = {10.1216/rmjm/1194275937},
   Key = {fds302442}
}

@article{fds302440,
   Author = {Hahn, H},
   Title = {On zeros of Eisenstein series for genus zero Fuchsian
             groups},
   Journal = {Proceedings of the American Mathematical
             Society},
   Volume = {135},
   Number = {8},
   Pages = {2391-2401},
   Publisher = {American Mathematical Society (AMS)},
   Year = {2007},
   Month = {August},
   ISSN = {0002-9939},
   url = {http://dx.doi.org/10.1090/S0002-9939-07-08763-1},
   Abstract = {Let Γ ≤ SL (ℝ) be a genus zero Fuchsian group of the
             first kind with ∞ as a cusp, and let E be the holomorphic
             Eisenstein series of weight 2k on Γ that is nonvanishing at
             ∞ and vanishes at all the other cusps (provided that such
             an Eisenstein series exists). Under certain assumptions on
             Γ, and on a choice of a fundamental domain F, we prove that
             all but possibly c(Γ, F) of the nontrivial zeros of E lie
             on a certain subset of {z ∈ h: jΓ(z) ∈ℝ}. Here c(Γ,
             F) is a constant that does not depend on the weight, h is
             the upper half-plane, and jΓ is the canonical hauptmodul
             for Γ. © 2007 American Mathematical Society Reverts to
             public domain 28 years from publication. 2 2k 2k Γ
             Gamma;},
   Doi = {10.1090/S0002-9939-07-08763-1},
   Key = {fds302440}
}

@article{fds302441,
   Author = {Ablowitz, MJ and Chakravarty, S and Hahn, H},
   Title = {Integrable systems and modular forms of level
             2},
   Journal = {Journal of Physics A: Mathematical and General},
   Volume = {39},
   Number = {50},
   Pages = {15341-15353},
   Publisher = {IOP Publishing},
   Year = {2006},
   Month = {December},
   ISSN = {0305-4470},
   url = {http://dx.doi.org/10.1088/0305-4470/39/50/003},
   Abstract = {A set of nonlinear differential equations associated with
             the Eisenstein series of the congruent subgroup Γ (2) of
             the modular group SL (ℤ) is constructed. These nonlinear
             equations are analogues of the well-known Ramanujan
             equations, as well as the Chazy and Darboux-Halphen
             equations associated with the modular group. The general
             solutions of these equations can be realized in terms of the
             Schwarz triangle function S(0, 0, 1/2; z). © 2006 IOP
             Publishing Ltd. 0 2},
   Doi = {10.1088/0305-4470/39/50/003},
   Key = {fds302441}
}

@article{fds302439,
   Author = {Hahn, H},
   Title = {Septic analogues of the Rogers-Ramanujan
             functions},
   Journal = {Acta Arithmetica},
   Volume = {110},
   Number = {4},
   Pages = {381-399},
   Publisher = {Institute of Mathematics, Polish Academy of
             Sciences},
   Year = {2003},
   Month = {January},
   url = {http://dx.doi.org/10.4064/aa110-4-5},
   Doi = {10.4064/aa110-4-5},
   Key = {fds302439}
}

@article{fds302438,
   Author = {Chan, HH and Hahn, H and Lewis, RP and Tan, SL},
   Title = {New Ramanujan-Kolberg type partition identities},
   Journal = {Mathematical Research Letters},
   Volume = {9},
   Number = {5-6},
   Pages = {801-811},
   Publisher = {International Press of Boston},
   Year = {2002},
   Month = {January},
   url = {http://dx.doi.org/10.4310/mrl.2002.v9.n6.a8},
   Abstract = {In this article, we use functions studied by N. J. Fine and
             R. J. Evans to construct analogues of modular equations
             first discovered by S. Ramanujan. We then use these
             functions to construct new identities satisfied by Σ
             p(ln+k)q , with odd prime l and 0 ≤ k ≤ (l - 1). Our new
             partition identities are inspired by the work of O. Kolberg
             and Ramanujan. n=0 ∞ n},
   Doi = {10.4310/mrl.2002.v9.n6.a8},
   Key = {fds302438}
}


%% Papers Accepted   
@article{fds305734,
   Author = {H. Hahn},
   Title = {On tensor thrid L-functions of automorphic representations
             of GL_n(A_F)},
   Journal = {Proc. Amer. Math. Soc.},
   Year = {2016},
   Key = {fds305734}
}


%% Papers Submitted   
@article{fds227060,
   Author = {H. Hahn},
   Title = {On classical groups detected by the triple tensor product
             and the Littlewood-Richardson semigroup},
   Year = {2016},
   Key = {fds227060}
}

 

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