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Asymptotic formulas for the coefficients of the truncated theta series

2024/08/18 by Mao, Renrong
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.09467

Abstract

Motivated by the groundbreaking work of Andrews and Merca, truncated theta series have been extensively studied over the years. In particular, 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 truncated theta series and prove that Merca's conjectures are true for sufficiently large N.

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