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

  • BERNARD L. S. LIN (a1)

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  $4n+3$ .

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

  • BERNARD L. S. LIN (a1)

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