Rationality and p-adic properties of reduced forms of half-integral weight
Number Theory
2018-07-09 v1
Abstract
In this paper we study special bases of certain spaces of half-integral weight weakly holomorphic modular forms. We establish a criterion for the integrality of Fourier coefficients of such bases. By using recursive relations between Hecke operators, we derive relations of Fourier coefficients of each basis element and obtain congruences of the Fourier coefficients, which extend known congruences for traces of singular moduli.
Keywords
Cite
@article{arxiv.1807.02454,
title = {Rationality and p-adic properties of reduced forms of half-integral weight},
author = {Suh Hyun Choi and Chang Heon Kim and Yeong-Wook Kwon and Kyu-Hwan Lee},
journal= {arXiv preprint arXiv:1807.02454},
year = {2018}
}
Comments
19 pages