On the vanishing of coefficients of the powers of a theta function

Jacques Sauloy; Changgui Zhang

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arXiv · 2007.16092

On the vanishing of coefficients of the powers of a theta function

Jacques Sauloy·Changgui Zhang

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Abstract

A result on the Galois theory of $q$-difference equations \cite{JSTALPAEN} leads to the following question: if $q \in \Cs$, $\lmod q \rmod < 1$ and if one sets $\thq(z) := \sum\limits_{m \in \Z} q^{m(m-1)/2} z^m$, can some coefficients of the Laurent series expansion of $\theta_q^k(z)$, $k \in \N^*$, vanish ? We give a partial answer.

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Jacques Sauloy, Changgui Zhang. 2020-07-31. On the vanishing of coefficients of the powers of a theta function. https://arxiv.org/abs/2007.16092

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