Results 71 to 80 of about 230 (149)
, 2018 We define canonical real analytic versions of modular forms of integral weight for the full modular group, generalising real analytic Eisenstein series. They are harmonic Maass waveforms with poles at the cusp, whose Fourier coefficients involve periods ...
Brown, Francis, Brown, FCS
core +1 more source
Spaces of Weakly Holomorphic Modular Forms in Level 52
, 2017 Let M#k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S#k(52) the subspace of forms which vanish at all cusps other than infinity.
Adams, Daniel Meade
core
Regularized inner products and meromorphic modular forms
, 2017 In this talk, we discuss regularized inner products between meromorphic modular forms. In addition to their established applications via theta lifts, we will introduce a realization of higher Green’s functions evaluated at CM-points as an inner product ...
Kane, BR
core +1 more source
A Note on Estimates of Fourier Coefficients of Weakly Holomorphic Modular Forms
, 2012 Here, we give a detailed account of a proof for the estimates of Fourier coefficients of weakly holomorphic modular forms, which play an important role in the study of Borcherds lifts.departmental bulletin ...
MURASE, Atsushi +5 more
core
REGULARIZED PETERSSON INNER PRODUCTS FOR MEROMORPHIC MODULAR FORMS (Automorphic Forms, Automorphic L-Functions and Related Topics) [PDF]
, 2017 We investigate the history of inner products within the theory of modular forms. We first give the history of the applications of Petersson 's original definition for the inner product of S_{2k} and then recall Zagier' s extension to a nondegenerate (but
Kane, Ben
core
Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras
Transactions of the American Mathematical Society, 2015 In this paper, we compute basis elements of certain spaces of weight 0 0 weakly holomorphic modular forms and consider the ...
Kim, Henry H. +2 more
openaire +3 more sources
The arithmetic of modular grids
, 2022 A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved this coefficient
Griffin, Michael +2 more
core
Eichler–Shimura theory for mock modular forms
, 2020 We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the "extra relation" that is satisfied by even periods of ...
Kathrin Bringmann +3 more
core
A single-variable proof of the omega SPT congruence family over powers of 5. [PDF]
Ramanujan J, 2023 Smoot NA.
europepmc +1 more source
Coefficients of modular forms and applications to partition theory
, 2023 We begin with an overview of the theory of modular forms as well as some relevant sub-topics in order to discuss three results: the first result concerns positivity of self-conjugate t-core partitions under the assumption of the Generalized Riemann ...
Hanson, Michael Anthony
core