Ramanujan type congruences for quotients of level 7 Klein forms

Authors

Timothy Huber, The University of Texas Rio Grande ValleyFollow
Dongxi Ye

Document Type

Article

Publication Date

5-2021

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

Original published version available at https://doi.org/10.1016/j.jnt.2020.11.003

Recommended Citation

Huber, Timothy, and Dongxi Ye. "Ramanujan type congruences for quotients of level 7 Klein forms." Journal of Number Theory 222 (2021): 181-203. https://doi.org/10.1016/j.jnt.2020.11.003

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Journal of Number Theory

DOI

10.1016/j.jnt.2020.11.003