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ARITHMETIC PROPERTIES OF COEFFICIENTS OF THE MOCK THETA FUNCTION $B(q)$

Part of: Additive number theory; partitions Combinatorics

Published online by Cambridge University Press:  21 November 2019

RENRONG MAO Open the ORCID record for RENRONG MAO [Opens in a new window]
RENRONG MAO*
Affiliation:
Department of Mathematics,Soochow University, SuZhou 215006, PR China email rrmao@suda.edu.cn
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Abstract

We investigate the arithmetic properties of the second-order mock theta function $B(q)$ and establish two identities for the coefficients of this function along arithmetic progressions. As applications, we prove several congruences for these coefficients.

Keywords

mock theta functioncongruencegeneralised Lambert seriestheta function

MSC classification

Primary: 11P83: Partitions; congruences and congruential restrictions
Secondary: 05A17: Partitions of integers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 50 - 58
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The author was partially supported by the National Natural Science Foundation of China (Grant No. 11971341).

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