most citedModular forms, de Rham cohomology and congruences

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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…

math.NT2012

Modular parametrizations of certain elliptic curves

Matija Kazalicki, Yuichi Sakai, Koji Tasaka

Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a parti…