Congruences for the coefficients of the Gordon and McIntosh mock theta function ξ(q)

Robson da Silva; James A. Sellers

doi:10.1007/s11139-021-00479-8

Congruences for the coefficients of the Gordon and McIntosh mock theta function ξ(q)

Robson da Silva
, James A. Sellers

Mathematics & Statistics

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

10 Scopus citations

Abstract

Recently Gordon and McIntosh introduced the third order mock theta function ξ(q) defined by ξ(q)=1+2∑n=1∞q6n2-6n+1(q;q6)n(q5;q6)n.Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan-like congruences.

Original language	English (US)
Pages (from-to)	815-834
Number of pages	20
Journal	Ramanujan Journal
Volume	58
Issue number	3
DOIs	https://doi.org/10.1007/s11139-021-00479-8
State	Published - Jul 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Congruence
Generating function
Mock theta function

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10.1007/s11139-021-00479-8

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abstract = "Recently Gordon and McIntosh introduced the third order mock theta function ξ(q) defined by ξ(q)=1+2∑n=1∞q6n2-6n+1(q;q6)n(q5;q6)n.Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan-like congruences.",

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AU - da Silva, Robson

AU - Sellers, James A.

PY - 2022/7

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N2 - Recently Gordon and McIntosh introduced the third order mock theta function ξ(q) defined by ξ(q)=1+2∑n=1∞q6n2-6n+1(q;q6)n(q5;q6)n.Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan-like congruences.

AB - Recently Gordon and McIntosh introduced the third order mock theta function ξ(q) defined by ξ(q)=1+2∑n=1∞q6n2-6n+1(q;q6)n(q5;q6)n.Our goal in this paper is to study arithmetic properties of the coefficients of this function. We present a number of such properties, including several infinite families of Ramanujan-like congruences.

KW - Congruence

KW - Generating function

KW - Mock theta function

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JF - Ramanujan Journal

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ER -

Congruences for the coefficients of the Gordon and McIntosh mock theta function ξ(q)

Abstract

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