Fast computation of half-integral weight modular forms

Abstract

To study statistical properties of modular forms, including for instance Sato-Tate like problems, it is essential to have a large number of Fourier coefficients. In this article, we exhibit three bases for the space of modular forms of any half-integral weight and level 4, which have the property that many coefficients can be computed (relatively) quickly on a computer.

v3, 6 pages; added rough complexity estimate

References in corpus (1)

• On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture

Cited by in corpus (2)

• On the distribution of coefficients of half-integral weight modular forms and the Bruinier-Kohnen Conjecture
• Computing L-Functions of Quadratic Characters at Negative Integers