Arithmetic properties of septic partition functions

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
Mayra Huerta, The University of Texas Rio Grande Valley
Nathaniel Mayes, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

1-16-2021

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. Ramanujan's partition congruence modulo 7 serves as a prototype for the process used to prove new congruences for modular forms of level 7.

Comments

Electronic version of an article published as International Journal of Number Theory 2021, doi.org/10.1142/S179304212040031X © World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijnt

Recommended Citation

Huber, T., Huerta, M., & Mayes, N. (2021). Arithmetic properties of septic partition functions. International Journal of Number Theory. https://doi.org/10.1142/S179304212040031X

Publication Title

International Journal of Number Theory

DOI

10.1142/S179304212040031X