BYU

Abstract by Ryan Keck

Personal Infomation


Presenter's Name

Ryan Keck

Degree Level

Masters

Abstract Infomation


Department

Mathematics

Faculty Advisor

Paul Jenkins

Title

Congruences for Coefficients of Modular Forms in Levels 3, 5, and 7 with Poles at 0

Abstract

Let Mk(N) be the space of weakly holomorphic modular forms that are holomorphic away from the cusp at 0. We prove congruences modulo powers of 3, 5, and 7 for the Fourier coefficients of weight 0 forms in the spaces where N = 3, 5, 7 respectively. We conjecture that these congruences can be improved to a congruence involving counting the number of times certain digits appear in the base N expansion of the modular form's order of vanishing at infinity.