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International Conference "Analytic Theory of Differential and Difference Equations" Dedicated to the Memory of Andrey Bolibrukh
February 3, 2021 19:00, online, Moscow
 


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

Changgui Zhang

Université de Lille, Departement de Mathématique
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Abstract: A result on the Galois theory of $q$-difference equations leads to the following question: if $0<|q|<1$ and if one sets
$$ \theta_q(z):=\sum\limits_{m\in\mathbb{Z}} q^{m(m-1)/2} z^m, $$
can some coefficients of the Laurent series expansion of $\theta_q^n(z)$, $n \in \mathbb{N}^*$, vanish? We give a partial answer. This is a joint work with Jacques Sauloy (see arXiv:2007.16092[math.DS]).

Language: English

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