OVERPARTITIONS RELATED TO THE MOCK THETA FUNCTION

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 $4n+3$ .