Asymptotics for the coefficients of the truncated theta series

Renrong Mao

Applied Mathematics and Computation, 2025, vol. 507, issue C

Abstract: Motivated by the groundbreaking work of Andrews and Merca, truncated theta series are extensively studied in recent years. Recently, Merca made conjectures on the non-negativity of the coefficient of qN in truncated series from the Jacobi triple product identity and the quintuple product identity. In this paper, using Wright's Circle Method, we establish asymptotic formulas for the coefficients of these series and prove Merca's conjectures are true for sufficiently large N.

Keywords: Truncated theta series; The Jacobi triple product identity; The quintuple product identity; Asymptotic inequality; Circle method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325003182

DOI: 10.1016/j.amc.2025.129592

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