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OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION
$V_{0}(q)$
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 102 / Issue 3 / December 2020
- Published online by Cambridge University Press:
- 16 January 2020, pp. 410-417
- Print publication:
- December 2020
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- Article
- Export citation
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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 
$4n+3$.
