Results 21 to 30 of about 353 (48)

Euler-like recurrences for smallest parts functions [PDF]

, 2014
We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function.
In Memory Of Basil Gordon, Nickolas Andersen, Scott Ahlgren   +2 more
core   +1 more source

Partial theta functions and mock modular forms as q-hypergeometric series [PDF]

, 2011
Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms.
Bringmann, Kathrin, Folsom, Amanda, Rhoades, Robert C.   +2 more
core   +1 more source

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 [PDF]

, 2013
We prove that the coefficients of certain mock theta functions possess no linear congruences modulo 3. We prove similar results for the moduli 2 and 3 for a wide class of weakly holomorphic modular forms and discuss applications.
Ahlgren, Scott, Kim, Byungchan
core   +1 more source

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

Generating weights for the Weil representation attached to an even order cyclic quadratic module [PDF]

, 2017
We develop geometric methods to study the generating weights of free modules of vector valued modular forms of half-integral weight, taking values in a complex representation of the metaplectic group.
Candelori, Luca, Franc, Cameron, Kopp, Gene S.   +2 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

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

Non-vanishing of $L$-functions associated to cusp forms of half-integral weight

, 2013
In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W.
G. Shimura, H. Iwaniec, M. Manickam, M. Manickam, N. Koblitz, N. Kumar, W. Kohnen, W. Kohnen   +7 more
core   +1 more source