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VANISHING COEFFICIENTS IN QUOTIENTS OF THETA FUNCTIONS OF MODULUS FIVE

Part of: Discontinuous groups and automorphic forms Series expansions

Published online by Cambridge University Press:  27 March 2020

SHANE CHERN Open the ORCID record for SHANE CHERN [Opens in a new window]  and
DAZHAO TANG
SHANE CHERN
Affiliation:
Department of Mathematics,Penn State University, University Park, PA 16802, USA email shanechern@psu.edu
DAZHAO TANG*
Affiliation:
Center for Applied Mathematics,Tianjin University, Tianjin 300072, PR China email dazhaotang@sina.com
*
✉dazhaotang@sina.com
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Abstract

Following recent investigations of vanishing coefficients in infinite products, we show that such instances are very rare when the infinite product is among a family of theta-quotients of modulus five. We also prove that a general family of products of theta functions of modulus five can always be effectively 5-dissected.

Keywords

theta functionsvanishing coefficients5-dissections

MSC classification

Primary: 11F27: Theta series; Weil representation; theta correspondences
Secondary: 30B10: Power series (including lacunary series)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 387 - 398
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author was supported by the Postdoctoral Science Foundation of China (No. 2019M661005).

References

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