Extension of a proof of the Ramanujan congruences for multipartitions

Oleg Lazarev; Matthew S. Mizuhara; Benjamin Reid; Holly Swisher

doi:10.1007/s11139-016-9817-x

Extension of a proof of the Ramanujan congruences for multipartitions

Oleg Lazarev
, Matthew S. Mizuhara
, Benjamin Reid
, Holly Swisher

Mathematics

Stanford University
Pennsylvania State University
University of Oregon
Oregon State University

Research output: Contribution to journal › Article › peer-review

Abstract

Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function p(n). Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without the need for Hecke operators. In this paper, we give a method for generalizing Lachterman, Schayer, and Younger’s proof to include Ramanujan congruences for multipartition functions p_k(n) and Ramanujan congruences for p(n) modulo certain prime powers.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Ramanujan Journal
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s11139-016-9817-x
State	Published - Jan 1 2018

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Congruences
Multipartitions
Partitions
Ramanujan

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10.1007/s11139-016-9817-x

Cite this

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abstract = "Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function p(n). Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without the need for Hecke operators. In this paper, we give a method for generalizing Lachterman, Schayer, and Younger{\textquoteright}s proof to include Ramanujan congruences for multipartition functions pk(n) and Ramanujan congruences for p(n) modulo certain prime powers.",

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AU - Mizuhara, Matthew S.

AU - Reid, Benjamin

AU - Swisher, Holly

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Y1 - 2018/1/1

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AB - Recently Lachterman, Schayer, and Younger published an elegant proof of the Ramanujan congruences for the partition function p(n). Their proof uses only the classical theory of modular forms as well as a beautiful result of Choie, Kohnen, and Ono, without the need for Hecke operators. In this paper, we give a method for generalizing Lachterman, Schayer, and Younger’s proof to include Ramanujan congruences for multipartition functions pk(n) and Ramanujan congruences for p(n) modulo certain prime powers.

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KW - Multipartitions

KW - Partitions

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Extension of a proof of the Ramanujan congruences for multipartitions

Abstract

ASJC Scopus Subject Areas

Keywords

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