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

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

2011-06-06

arxiv.org/abs/1106.1188v1

Mathematics

Number Theory

Scientific paper

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

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