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Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes (1106.1188v1)
Published 6 Jun 2011 in math.NT
Abstract: 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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