%% 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 = {9780821839737},
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 = {02},
Pages = {479-486},
Publisher = {World Scientific Publishing},
Year = {2021},
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 products
and the Littlewood-Richardson semigroup},
Journal = {Reserch in Number Theory},
Volume = {2},
Number = {1},
Pages = {1-12},
Publisher = {Springer Nature},
Year = {2016},
Month = {June},
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 n that stabilize a line in a given repesentation of GL
n. 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 n is
the triple tensor product representation ⊗ 3. We prove a
family of results describing when subgroups isomorphic to
classical groups of type Bn, Cn, D2n are
detected.},
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, ⊗3), where π is a cuspidal
automorphic representation of GLn(AF)and F is a global
field.},
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 = {Contemporary Mathematics},
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 = {Int. Math. Res. Not.},
Volume = {2009},
Number = {21},
Pages = {3957-3978},
Publisher = {Oxford University Press},
Year = {2009},
Month = {June},
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 Gamma_0(2)},
Journal = {Ramanujan J.},
Volume = {15},
Number = {2},
Pages = {235-257},
Year = {2008},
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 Γ0(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 Γ0(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.},
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 σ̃s (n)
= Σd/n (-1)d-1ds and σ̂ s = Σd/n(-l)(n/d)-1ds, 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 σ̃3(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 s(n) and rs(n), s = 4, 8, in terms of σ̃(n),
σ̂(n), and σ̃3(n), where rs(n) denotes the number of
representations of n as a sum of s squares and δs(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.},
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 ≤ SL2(ℝ) be a genus zero Fuchsian group of the
first kind with ∞ as a cusp, and let EΓ2k 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 EGamma;2k 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.},
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 Γ0(2) of
the modular group SL2(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.},
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 Σn=0∞
p(ln+k)qn, with odd prime l and 0 ≤ k ≤ (l - 1). Our new
partition identities are inspired by the work of O. Kolberg
and Ramanujan.},
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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Mathematics Department