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arXiv · 1106.1188

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

Nickolas Andersen·Paul Jenkins
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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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Nickolas Andersen, Paul Jenkins. 2011-06-06. Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes. https://arxiv.org/abs/1106.1188

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