Modular forms, hypergeometric functions and congruences (CROSBI ID 192217)
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Podaci o odgovornosti
Kazalicki, Matija
engleski
Modular forms, hypergeometric functions and congruences
Using the theory of Stienstra and Beukers (Math. Ann., 271: 269-304, 1985), we prove that the numbers A(3)(n) and A(3)(n - 1) - 16A(3)(n - 2) satisfy three term congruence relations similar to those satisfied by Apery numbers. Moreover, for k >= 3 and p prime, we prove divisibility by p of some simple linear combinations of the numbers Ak(n), for n is an element of N. To obtain this, we study the arithmetic properties of the Fourier coefficients of certain holomorphic and weakly holomorphic modular forms.
modular forms ; hypergeometric functions ; congruences
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