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تسجيل مستخدم جديدParity of coefficients of mock theta functions
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تأليف
Liuquan Wang
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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 $ngeq 0$. 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 $(frac{1}{2},frac{1}{2})$ and 4 functions are of parity type $(frac{3}{4},frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of parity type $(1,0)$.
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