We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and Jenkins. The congruences involve a modulus that depends on the binary expansion of the modular form's order of vanishing at infinity. We also demonstrate congruences for Fourier coefficients of some level 4 modular functions.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Moss, Eric Brandon, "Congruences for Fourier Coefficients of Modular Functions of Levels 2 and 4" (2018). All Theses and Dissertations. 6952.
Weakly holomorphic modular forms, congruences, Fourier coefficients