Sign changes of coefficients of powers of the infinite Borwein product. (English) Zbl 1523.11181
It is denoted by \(c^{(m)}_t (n)\) the coefficient of \(q^n\) in the series expansion of
\[
(q; q)_m^\infty(q^t; q^t)^{-m}_\infty,
\]
which is the \(m\)-th power of the infinite Borwein product. Let \(t\) and \(m\) be positive integers with \(m(t-1)\leq 24\).
Asymptotic formulas are examined in one chapter, and non-asymptotic formulas in another. Very interesting results which are nicely well written.
Asymptotic formulas are examined in one chapter, and non-asymptotic formulas in another. Very interesting results which are nicely well written.
Reviewer: Rózsa Horváth-Bokor (Budakalász)
MSC:
| 11P55 | Applications of the Hardy-Littlewood method |
| 11F03 | Modular and automorphic functions |
| 11F30 | Fourier coefficients of automorphic forms |
| 26D15 | Inequalities for sums, series and integrals |
| 26D20 | Other analytical inequalities |
Keywords:
sign changes; vanishing coefficients; eta products; hauptmodul; theta functions; asymptoticsReferences:
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