A generalized Hardy-Ramanujan formula for the number of restricted integer partitions

Tiefeng Jiang, Ke Wang

Research output: Contribution to journalArticle

Abstract

We derive an asymptotic formula for p n (N,M), the number of partitions of integer n with part size at most N and length at most M. We consider both N and M are comparable to n. This is an extension of the classical Hardy-Ramanujan formula and Szekeres’ formula. The proof relies on the saddle point method.

Original languageEnglish (US)
JournalJournal of Number Theory
DOIs
StatePublished - Jan 1 2019

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Integer Partitions
Ramanujan
Saddle Point Method
Asymptotic Formula
Partition
Integer

Keywords

  • Asymptotic formula
  • Restricted integer partitions

Cite this

A generalized Hardy-Ramanujan formula for the number of restricted integer partitions. / Jiang, Tiefeng; Wang, Ke.

In: Journal of Number Theory, 01.01.2019.

Research output: Contribution to journalArticle

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