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OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION $V_{0}(q)$

Part of: Combinatorics Additive number theory; partitions

Published online by Cambridge University Press:  16 January 2020

BERNARD L. S. LIN Open the ORCID record for BERNARD L. S. LIN [Opens in a new window]
BERNARD L. S. LIN*
Affiliation:
School of Science, Jimei University, Xiamen361021, PR China email linlsjmu@163.com
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Abstract

Recently, Brietzke, Silva and Sellers [‘Congruences related to an eighth order mock theta function of Gordon and McIntosh’, J. Math. Anal. Appl.479 (2019), 62–89] studied the number $v_{0}(n)$ of overpartitions of $n$ into odd parts without gaps between the nonoverlined parts, whose generating function is related to the mock theta function $V_{0}(q)$ of order 8. In this paper we first present a short proof of the 3-dissection for the generating function of $v_{0}(2n)$. Then we establish three congruences for $v_{0}(n)$ along certain progressions which are subsequences of the integers $4n+3$.

Keywords

partitionoverpartition into odd partscongruencesmock theta 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 3 , December 2020 , pp. 410 - 417
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by the National Natural Science Foundation of China (no. 11871246), the Natural Science Foundation of Fujian Province of China (no. 2019J01328) and the Program for New Century Excellent Talents in Fujian Province University (no. B17160).

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