A generalization of the modular equations of higher degrees

Sun Kim

doi:10.1016/j.jcta.2021.105420

A generalization of the modular equations of higher degrees

Sun Kim

Department of Mathematics

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

3 Scopus citations

Abstract

Ramanujan's modular equations of prime degrees 3,5,7,11 and 23 are associated with elegant colored partition theorems. In 2005, S. O. Warnaar established a general identity which implies the modular equations of degrees 3 and 7. In this paper, we provide a generalization of the remaining modular equations of degrees 5,11 and 23. In addition, we derive many partition identities from the generalization.

Original language	English
Article number	105420
Journal	Journal of Combinatorial Theory. Series A
Volume	180
DOIs	https://doi.org/10.1016/j.jcta.2021.105420
State	Published - 2021.05

Keywords

Colored partitions
Modular equations
Theta functions

Quacquarelli Symonds(QS) Subject Topics

Computer Science & Information Systems
Mathematics

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10.1016/j.jcta.2021.105420

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title = "A generalization of the modular equations of higher degrees",

abstract = "Ramanujan's modular equations of prime degrees 3,5,7,11 and 23 are associated with elegant colored partition theorems. In 2005, S. O. Warnaar established a general identity which implies the modular equations of degrees 3 and 7. In this paper, we provide a generalization of the remaining modular equations of degrees 5,11 and 23. In addition, we derive many partition identities from the generalization.",

keywords = "Colored partitions, Modular equations, Theta functions",

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year = "2021",

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N2 - Ramanujan's modular equations of prime degrees 3,5,7,11 and 23 are associated with elegant colored partition theorems. In 2005, S. O. Warnaar established a general identity which implies the modular equations of degrees 3 and 7. In this paper, we provide a generalization of the remaining modular equations of degrees 5,11 and 23. In addition, we derive many partition identities from the generalization.

AB - Ramanujan's modular equations of prime degrees 3,5,7,11 and 23 are associated with elegant colored partition theorems. In 2005, S. O. Warnaar established a general identity which implies the modular equations of degrees 3 and 7. In this paper, we provide a generalization of the remaining modular equations of degrees 5,11 and 23. In addition, we derive many partition identities from the generalization.

KW - Colored partitions

KW - Modular equations

KW - Theta functions

UR - https://www.scopus.com/pages/publications/85100243655

U2 - 10.1016/j.jcta.2021.105420

DO - 10.1016/j.jcta.2021.105420

M3 - Journal article

AN - SCOPUS:85100243655

SN - 0097-3165

VL - 180

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

M1 - 105420

ER -

A generalization of the modular equations of higher degrees

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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