An infinite family of congruences arising from a second order mock theta function

Abstract

Let β(q) = n≥0 b(n)q n be a second order mock theta function defined by n≥0 q n(n+1) (−q 2 ; q 2 )n (q; q 2 ) 2 n+1 .In this paper, we obtain an infinite family of congruences modulo powers of 3 for b(n).

Parity of coefficients of mock theta functions

“…Several congruences for c(ω (3) ; n) and c(ν (3) ; n) modulo 11 were also presented in [46]. For more congruences satisfied by coefficients of mock theta functions, see the works of Berg et al [7], Brietzke, Silva and Sellers [12], Chern and Wang [16], Mao [37] and Xia [49], for example. For any formal power series g(q) as in (1.10), we define its type modulo a positive integer as follows.…”