Parity of coefficients of mock theta functions

JOURNAL OF NUMBER THEORY

卷:229

Article

Wang, Liuquan¹ 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

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

DOI  :  10.1016/j.jnt.2021.04.023

来源: Elsevier

【 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.

【 授权许可】

Free