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math.NT2013★ 1 cited
Modular forms, hypergeometric functions and congruences
Matija Kazalicki
Using the theory of Stienstra and Beukers, we prove various elementary congruences for the numbers \sum \binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in…
math.NT2013★ 3 cited
Modular forms, de Rham cohomology and congruences
Matija Kazalicki, Anthony J. Scholl
In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of…