Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions

JOURNAL OF NUMBER THEORY

卷:216

Article

O'Sullivan, Cormac¹ 

[1] CUNY, Grad Ctr, Dept Math, 365 Fifth Ave, New York, NY 10016 USA

关键词: Partitions;    Asymptotics;    Sylvester waves;   

DOI  :  10.1016/j.jnt.2020.04.005

来源: Elsevier

【 摘 要 】

The generating function for restricted partitions is a finite product with a Laurent expansion at each root of unity. The question of the behavior of these Laurent coefficients as the size of the product increases goes back to Rademacher and his work on partitions. Building on the methods of Drmota, Gerhold and previous results of the author, we complete this description and give the full asymptotic expansion of each coefficient at every root of unity. These techniques are also shown to give the asymptotics of Sylvester waves. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free