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arXiv · 0910.0070

On the non-existence of simple congruences for quotients of Eisenstein series

Michael Dewar
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Abstract

A recent article of Berndt and Yee found congruences modulo 3^k for certain ratios of Eisenstein series. For all but one of these, we show there are no simple congruences a(pn+c) = 0 modulo p when p>= 13 is prime. This follows from a more general theorem on the non-existence of congruences in (E_2^r)(E_4^s)(E_6^t) where r is non-negative and r,s,t are integers.

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Michael Dewar. 2009-10-01. On the non-existence of simple congruences for quotients of Eisenstein series. https://arxiv.org/abs/0910.0070

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