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- W4287515077 abstract "We denote by $c_t^{(m)}(n)$ the coefficient of $q^n$ in the series expansion of $(q;q)_infty^m(q^t;q^t)_infty^{-m}$, which is the $m$-th power of the infinite Borwein product. Let $t$ and $m$ be positive integers with $m(t-1)leq 24$. We provide asymptotic formula for $c_t^{(m)}(n)$, and give characterizations of $n$ for which $c_t^{(m)}(n)$ is positive, negative or zero. We show that $c_t^{(m)}(n)$ is ultimately periodic in sign and conjecture that this is still true for other positive integer values of $t$ and $m$. Furthermore, we confirm this conjecture in the cases $(t,m)=(2,m),(p,1),(p,3)$ for arbitrary positive integer $m$ and prime $p$." @default.
- W4287515077 created "2022-07-25" @default.
- W4287515077 creator A5083505257 @default.
- W4287515077 date "2021-08-09" @default.
- W4287515077 modified "2023-10-17" @default.
- W4287515077 title "Sign Changes of Coefficients of Powers of the Infinite Borwein Product" @default.
- W4287515077 doi "https://doi.org/10.48550/arxiv.2108.03932" @default.
- W4287515077 hasPublicationYear "2021" @default.
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