Results 31 to 40 of about 346 (52)

q-hypergeometric double sums as mock theta functions [PDF]

, 2012
Recently, Bringmann and Kane established two new Bailey pairs and used them to relate certain q-hypergeometric series to real quadratic fields. We show how these pairs give rise to new mock theta functions in the form of q-hypergeometric double sums ...
Andrews, Jeremy Lovejoy, Ono, Robert Osburn, Warnaar, Zagier   +5 more
core   +3 more sources

On two 10th order mock theta identities

, 2013
We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.Comment: 5 pages, to appear in the Ramanujan ...
A. Folsom, B. Gordon, D. Hickerson, G.E. Andrews, Jeremy Lovejoy, R.J. McIntosh, Robert Osburn, S. Ramanujan, Y.-S. Choi   +8 more
core   +3 more sources

Eichler–Selberg relations for singular moduli

Forum of Mathematics, Sigma
The Eichler–Selberg trace formula expresses the trace of Hecke operators on spaces of cusp forms as weighted sums of Hurwitz–Kronecker class numbers. We extend this formula to a natural class of relations for traces of singular moduli, where one views ...
Yuqi Deng, Toshiki Matsusaka, Ken Ono
doaj   +1 more source

On cycle integrals of weakly holomorphic modular forms [PDF]

, 2014
In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms.
Bringmann, Kathrin, Guerzhoy, Pavel, Kane, Ben   +2 more
core   +3 more sources

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
doaj   +1 more source

Congruences for traces of singular moduli

, 2004
We extend a result of Ahlgren and Ono on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.Comment: 8 pages, to appear in The Ramanujan ...
Osburn, Robert
core   +1 more source

Equidistribution of signs for Hilbert modular forms of half-integral weight

, 2018
We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence.
Kaushik, Surjeet, Kumar, Narasimha, Tanabe, Naomi   +2 more
core   +1 more source

Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces II

, 1999
The purpose of this paper is to derive that the square of Fourier coe‰cients aðnÞ at a square free positive integer n of modular forms f of half integral weight belonging to Kohnen’s spaces of arbitrary odd level and of arbitrary primitive character is ...
H. Kojima
semanticscholar   +1 more source

Taylor coefficients of non-holomorphic Jacobi forms and applications

, 2017
In this paper, we prove modularity results of Taylor coefficients of certain non-holomorphic Jacobi forms. It is well-known that Taylor coefficients of holomorphic Jacobi forms are quasimoular forms.
Bringmann, Kathrin
core   +1 more source

Unramified Whittaker functions on the metaplectic group

, 1987
Kazhdan (unpublished), Shintani [Sh] and Casselman and Shalika [CS] computed explicitly the unramified Whittaker function of a quasisplit p-adic group. This is the main local ingredient used in the RankinSelberg-Shimura method, which yielded interesting ...
Y. Flicker
semanticscholar   +1 more source