Towards an automation of the circle method
Number Theory
2020-01-28 v1 Combinatorics
Abstract
The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of \emph{Mathematica} are presented along with results of a test for their numerical accuracy.
Cite
@article{arxiv.2001.09568,
title = {Towards an automation of the circle method},
author = {Andrew V. Sills},
journal= {arXiv preprint arXiv:2001.09568},
year = {2020}
}
Comments
18 pp., this version incorporates corrections to the published version suggested to the author by Michael Schlosser in an email dated January 20, 2020