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arXiv 2001.095682020-01-27math.NTmath.CO

Towards an automation of the circle method

Andrew V. Sills

备注：: 18 pp., this version incorporates corrections to the published version suggested to the author by Michael Schlosser in an email dated January 20, 2020
发表信息：: Gems in Experimental Mathematics, ed. T. Amdeberhan, L. Medina, and V. Moll; Contemporary Mathematics 517 (2010) 321--338

英文摘要：

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ 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.

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