Disproof of a conjecture by Rademacher on partial fractions

DOI10.1090/S2330-1511-2014-00014-6zbMath1339.11087arXiv1312.4289OpenAlexW2964063251WikidataQ123007333 ScholiaQ123007333MaRDI QIDQ2814367

Michael Drmota, Stefan Gerhold

Publication date: 21 June 2016

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4289

zbMATH Keywords

Mellin transformpolylogarithminteger partitionspartial fraction decompositionsaddle point asymptotics

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Analytic theory of partitions (11P82)

Related Items (5)

Partitions and Sylvester waves ⋮ Zeros of the dilogarithm ⋮ Asymptotics for the partial fractions of the restricted partition generating function I ⋮ Asymptotic expansion of Mathieu power series and trigonometric Mathieu series ⋮ Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions

Uses Software

• HANS

Cites Work

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• Mellin transforms and asymptotics: Harmonic sums
• The Rademacher conjecture and \(q\)-partial fractions
• Partitions: At the interface of \(q\)-series and modular forms
• Rational Approximations to the Dilogarithm
• On Rademacher's Conjecture and A Recurrence Relation of Euler
• Rademacher's infinite partial fraction conjecture is (almost certainly) false
• Asymptotic estimates for some number-theoretic power series

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