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

2009/10/01 by Michael Dewar, Dewar, Michael
Mathematics · #11F33 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33

paper · pdf · doi:10.48550/arxiv.0910.0070

7 pages

arxiv created 2009/10/01 · openalex publication_date 2009/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (E₂^r)(E₄^s)(E₆^t) where r is non-negative and r,s,t are integers.

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