PERIODICITIES FOR TAYLOR COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS



Guerzhoy, Pavel, Mertens, Michael H and Rolen, Larry
(2020) PERIODICITIES FOR TAYLOR COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS. PACIFIC JOURNAL OF MATHEMATICS, 307 (1). 137 - 157.

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Abstract

Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Taylor expansions around points in the upper half-plane, has been much less studied. Recently, Romik made a conjecture about the periodicity of coefficients around τ0=i of the classical Jacobi theta function θ3. Here, we generalize the phenomenon observed by Romik to a broader class of modular forms of half-integral weight and, in particular, prove the conjecture.

Item Type: Article
Uncontrolled Keywords: modular forms, Taylor coefficients, q-expansion principle, congruences
Depositing User: Symplectic Admin
Date Deposited: 07 Sep 2020 09:11
Last Modified: 09 Jan 2021 01:34
DOI: 10.2140/pjm.2020.307.137
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3100029