Document Type

Article

Publication Date

12-17-2020

Abstract

Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dissection formulas for the series imply Ramanujan type congruences modulo powers of 7 for a family of generating functions that subsume the counting function for 7-core partitions. The broad class of arithmetic functions considered here enumerate colored partitions by weights determined by parts modulo 7. The method is a prototype for similar analysis of modular forms of level 7 and at other prime levels. As an example of the utility of the dissection method, the paper concludes with a derivation of novel congruences for the number of representations by x^2+xy+2y^2 in exactly k ways.

Comments

© 2020 Elsevier Inc. All rights reserved. Original published version available at https://doi.org/10.1016/j.jnt.2020.11.003

Publication Title

Journal of Number Theory

DOI

10.1016/j.jnt.2020.11.003

Included in

Mathematics Commons

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