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 language | English (US) |
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Pages (from-to) | 322-353 |
Number of pages | 32 |
Journal | Journal of Number Theory |
Volume | 201 |
DOIs | |
State | Published - Aug 2019 |
Bibliographical note
Funding Information:The research of Tiefeng Jiang is supported in part by NSF Grant DMS-1209166 and DMS-1406279.Ke Wang is supported by HKUST Initiation Grant IGN16SC05.
Publisher Copyright:
© 2019 Elsevier Inc.
Keywords
- Asymptotic formula
- Restricted integer partitions