Disproof of a conjecture by Rademacher on partial fractions-Reference-Cited by-同舟云学术

Disproof of a conjecture by Rademacher on partial fractions

Published:2014-11-21 Issue:11 Volume:1 Page:121-134
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Drmota Michael,Gerhold Stefan

Abstract

In his book Topics in Analytic Number Theory (1973), Hans Rademacher considered the generating function of integer partitions into at most N N parts and conjectured certain limits for the coefficients of its partial fraction decomposition. We carry out an asymptotic analysis that disproves this conjecture, thus confirming recent observations of Sills and Zeilberger (Journal of Difference Equations and Applications 19 (2013)), who gave strong numerical evidence against the conjecture.

Publisher

American Mathematical Society (AMS)

Subject

General Medicine

Link

http://www.ams.org/bproc/2014-01-11/S2330-1511-2014-00014-6/S2330-1511-2014-00014-6.pdf

Reference16 articles.

1. Partitions: at the interface of 𝑞-series and modular forms;Andrews, George E.;Ramanujan J.,2003

2. Quantifier elimination for real closed fields by cylindrical algebraic decomposition;Collins, George E.,1975

3. On Rademacher’s conjecture and a recurrence relation of Euler;Davidson, Morley;Quaest. Math.,2002

4. Bibliotheca Mathematica, Vol. IV;de Bruijn, N. G.,1958

5. Function theory for Rogers-Ramanujan-like partition identities;Ehrenpreis, Leon,1993

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions;Journal of Number Theory;2020-11

2. Asymptotic expansion of Mathieu power series and trigonometric Mathieu series;Journal of Mathematical Analysis and Applications;2019-11

3. Partitions and Sylvester waves;The Ramanujan Journal;2017-09-12

4. Asymptotics for the partial fractions of the restricted partition generating function I;International Journal of Number Theory;2016-07-26

5. Zeros of the dilogarithm;Mathematics of Computation;2016-03-02