On a problem of Lehmer on partitions into squares

Michael D. Hirschhorn; James A. Sellers

doi:10.1007/s11139-004-0138-0

On a problem of Lehmer on partitions into squares

Michael D. Hirschhorn
, James A. Sellers

Mathematics

Research output: Contribution to journal › Review article › peer-review

5 Scopus citations

Abstract

In 1948 D.H.Lehmer published a brief work discussing the difference between representations of the integer n as a sum of squares and partitions of n into square summands. In this article we return to this topic and consider four partition functions involving square parts and prove various arithmetic properties of these functions. These results provide a natural extension to the work of Lehmer.

Original language	English (US)
Pages (from-to)	279-287
Number of pages	9
Journal	Ramanujan Journal
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/s11139-004-0138-0
State	Published - Sep 2004

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-004-0138-0

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abstract = "In 1948 D.H.Lehmer published a brief work discussing the difference between representations of the integer n as a sum of squares and partitions of n into square summands. In this article we return to this topic and consider four partition functions involving square parts and prove various arithmetic properties of these functions. These results provide a natural extension to the work of Lehmer.",

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AU - Sellers, James A.

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AB - In 1948 D.H.Lehmer published a brief work discussing the difference between representations of the integer n as a sum of squares and partitions of n into square summands. In this article we return to this topic and consider four partition functions involving square parts and prove various arithmetic properties of these functions. These results provide a natural extension to the work of Lehmer.

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UR - https://www.scopus.com/pages/publications/15544370275#tab=citedBy

U2 - 10.1007/s11139-004-0138-0

DO - 10.1007/s11139-004-0138-0

M3 - Review article

AN - SCOPUS:15544370275

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VL - 8

SP - 279

EP - 287

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

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On a problem of Lehmer on partitions into squares

Abstract

All Science Journal Classification (ASJC) codes

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