Parity of coefficients of mock theta functions

[摘要] We study the parity of coefficients of classical mock theta functions. Suppose g is a formal power series with integer coefficients, and let c(g; n) be the coefficient of q(n) in its series expansion. We say that g is of parity type (a, 1 - a) if c(g; n) takes even values with probability a for n >= 0. We show that among the 44 classical mock theta functions, 21 of them are of parity type (1, 0). We further conjecture that 19 mock theta functions are of parity type (1/2, 1/2 ) and 4 functions are of parity type (3/4, 1/4). We also give characterizations of n such that c(g; n) is odd for the mock theta functions of parity type (1, 0). (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-01

[关键词] Mock theta functions;Parity;Hecke-type series;Rogers-Ramanujan identities;Partitions