Posted in

Speaker:

Michael Mertens
Affiliation:

MPIM
Date:

Wed, 2019-05-15 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar 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 $\tau_0=i$ of the classical Jacobi theta function $\theta_3$.

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.

This is joint work with Pavel Guerzhoy and Larry Rolen.

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