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

2020/01/22 by Cormac O’Sullivan, O'Sullivan, Cormac
Mathematics · #11P82 #41A60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2001.08115

openalex publication_date 2020/01/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The generating function for restricted partitions is a finite product with a\nLaurent expansion at each root of unity. The question of the behavior of these\nLaurent coefficients as the size of the product increases goes back to\nRademacher and his work on partitions. Building on the methods of Drmota,\nGerhold and previous results of the author, we complete this description and\ngive the full asymptotic expansion of each coefficient at every root of unity.\nThese techniques are also shown to give the asymptotics of Sylvester waves.\n

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