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Arithmetic properties of septic partition functions

Timothy Huber

https://orcid.org/0000-0003-4943-3619

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

E-mail Address: timothy.huber@utrgv.edu

Corresponding author.

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Mayra Huerta

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

E-mail Address: mayra.huerta@utrgv.edu

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Nathaniel Mayes

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539, USA

E-mail Address: nathaniel.mayes01@utrgv.edu

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https://doi.org/10.1142/S179304212040031XCited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue I: In Honor of Bruce Berndt’s 80th Birthday
Editors: George E. Andrews, Michael Filaseta and Ae Ja Yee

Abstract

Congruences and related identities are derived for a set of colored and weighted partition functions whose generating functions generate the graded algebra of integer weight modular forms of level seven. The work determines a general strategy for identifying and proving identities and associated congruences for modular forms on the principal congruence subgroup of level $7$ $7$ . Ramanujan’s partition congruence modulo $7$ $7$ serves as a prototype for the process used to prove new congruences for modular forms of level $7$ $7$ .

Keywords:

AMSC: 11P82, 11P83, 11F33

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