English

Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes

Number Theory 2013-05-14 v1

Abstract

Lehner's 1949 results on the jj-invariant showed high divisibility of the function's coefficients by the primes p{2,3,5,7}p\in\{2,3,5,7\}. Expanding his results, we examine a canonical basis for the space of level pp modular functions holomorphic at the cusp 0. We show that the Fourier coefficients of these functions are often highly divisible by these same primes.

Keywords

Cite

@article{arxiv.1106.1188,
  title  = {Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes},
  author = {Nickolas Andersen and Paul Jenkins},
  journal= {arXiv preprint arXiv:1106.1188},
  year   = {2013}
}