%% Books
@book{fds320419,
Author = {Berndt, BC},
Title = {Ramanujan's Forty Identities for the RogersRamanujan
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 Lfunctions involving monomial
representations},
Journal = {International Journal of Number Theory},
Volume = {17},
Number = {2},
Pages = {479486},
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 Lfunctions 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 = {112},
Publisher = {Springer Nature},
Year = {2016},
Month = {December},
url = {http://dx.doi.org/10.1007/s4099301600493},
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/s4099301600493},
Key = {fds320417}
}
@article{fds320109,
Author = {Hahn, H},
Title = {On tensor third Lfunctions of automorphic representations
of GLn(AF)},
Journal = {Proceedings of the American Mathematical
Society},
Volume = {144},
Number = {12},
Pages = {50615069},
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
Lfunctions 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 = {99118},
Publisher = {Mathematical Sciences Publishers},
Year = {2015},
Month = {January},
ISSN = {00308730},
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 squarefree values of sequences associated
with elliptic curves},
Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
Later},
Volume = {606},
Pages = {171188},
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 = {116},
Publisher = {World Scientific Pub Co Pte Lt},
Year = {2013},
ISSN = {17930421},
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 ℓadic 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 = {39573978},
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 = {235257},
Year = {2008},
Month = {February},
url = {http://dx.doi.org/10.1007/s111390079075z},
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/s111390079075z},
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 = {15931622},
Publisher = {Rocky Mountain Mathematics Consortium},
Year = {2007},
Month = {December},
ISSN = {00357596},
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 d1
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 = {23912401},
Publisher = {American Mathematical Society (AMS)},
Year = {2007},
Month = {August},
ISSN = {00029939},
url = {http://dx.doi.org/10.1090/S0002993907087631},
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 halfplane, 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/S0002993907087631},
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 = {1534115353},
Publisher = {IOP Publishing},
Year = {2006},
Month = {December},
ISSN = {03054470},
url = {http://dx.doi.org/10.1088/03054470/39/50/003},
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 wellknown Ramanujan
equations, as well as the Chazy and DarbouxHalphen
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 = {10.1088/03054470/39/50/003},
Key = {fds302441}
}
@article{fds302439,
Author = {Hahn, H},
Title = {Septic analogues of the RogersRamanujan
functions},
Journal = {Acta Arithmetica},
Volume = {110},
Number = {4},
Pages = {381399},
Publisher = {Institute of Mathematics, Polish Academy of
Sciences},
Year = {2003},
Month = {January},
url = {http://dx.doi.org/10.4064/aa11045},
Doi = {10.4064/aa11045},
Key = {fds302439}
}
@article{fds302438,
Author = {Chan, HH and Hahn, H and Lewis, RP and Tan, SL},
Title = {New RamanujanKolberg type partition identities},
Journal = {Mathematical Research Letters},
Volume = {9},
Number = {56},
Pages = {801811},
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 Lfunctions 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 LittlewoodRichardson semigroup},
Year = {2016},
Key = {fds227060}
}
