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

2020/07/31 by Sauloy, Jacques, Zhang, Changgui
#33E30 #39A13 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.16092

Abstract

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

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