Some q-series identities extending work of Andrews, Crippa, and Simon\n on sums of divisors functions

2019/07/02 by Kathrin Bringmann, Bringmann, Kathrin, Chris Jennings-Shaffer +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1907.01236

openalex publication_date 2019/07/02 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

In this article we extend a theorem of Andrews, Crippa, and Simon on the\nasymptotic behavior of polynomials defined by a general class of recursive\nequations. Here the polynomials are in the variable q, and the recursive\ndefinition at step n introduces a polynomial in n. Our extension replaces\nthe polynomial in n with either an exponential or periodic function of n.\n

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