The space of convolution identities on divisor functions

Sungkon Chang

doi:10.1007/s11139-019-00190-9

The space of convolution identities on divisor functions

Sungkon Chang

Mathematical Sciences

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

2 Scopus citations

Abstract

We consider convolutions of divisor functions in arbitrary length with modular congruence restrictions, and introduce the notion of a space of convolution identities over the rational numbers. As a main result, we introduce a conjecture on the connection between the dimension of the space of convolution identities and the number of partitions of a positive integer into exactly three parts, and prove the conjecture for 15 cases. We also prove convolution identities in arbitrary length.

Original language	English
Pages (from-to)	659-677
Number of pages	19
Journal	Ramanujan Journal
Volume	54
Issue number	3
DOIs	https://doi.org/10.1007/s11139-019-00190-9
State	Published - Apr 2021

Scopus Subject Areas

Algebra and Number Theory

Keywords

Convolution identities
Convolution sums
Elliptic functions
Partitions into exactly k-parts

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10.1007/s11139-019-00190-9

Cite this

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title = "The space of convolution identities on divisor functions",

abstract = "We consider convolutions of divisor functions in arbitrary length with modular congruence restrictions, and introduce the notion of a space of convolution identities over the rational numbers. As a main result, we introduce a conjecture on the connection between the dimension of the space of convolution identities and the number of partitions of a positive integer into exactly three parts, and prove the conjecture for 15 cases. We also prove convolution identities in arbitrary length.",

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AB - We consider convolutions of divisor functions in arbitrary length with modular congruence restrictions, and introduce the notion of a space of convolution identities over the rational numbers. As a main result, we introduce a conjecture on the connection between the dimension of the space of convolution identities and the number of partitions of a positive integer into exactly three parts, and prove the conjecture for 15 cases. We also prove convolution identities in arbitrary length.

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KW - Convolution sums

KW - Elliptic functions

KW - Partitions into exactly k-parts

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DO - 10.1007/s11139-019-00190-9

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The space of convolution identities on divisor functions

Abstract

Scopus Subject Areas

Keywords

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