18 citations · 77 across the 18 of their papers we have counts for
22 papers
Lucas congruences using modular forms
Frits Beukers, Wei-Lun Tsai, Dongxi Ye
In this work, we prove that many Apéry-like sequences arising from modular forms satisfy the Lucas congruences modulo any prime. As an implication, we completely affirm four conjec…
Supercongruences using modular forms
Frits Beukers
Many generating series of combinatorially interesting numbers have the property that the sum of the terms of order at some suitable point is congruent to a zero of a zeta-func…
Frobenius structure and -adic zeta values
Frits Beukers, Masha Vlasenko
For differential operators of Calabi-Yau type, Candelas, de la Ossa and van Straten conjecture the appearance of -adic zeta values in the matrix entries of their -adic Froben…
-Linear schemes for sequences modulo
Frits Beukers
Many interesting combinatorial sequences, such as Apéry numbers and Franel numbers, enjoy the so-called Lucas property modulo almost all primes . Modulo prime powers such…
On -integrality of instanton numbers
Frits Beukers, Masha Vlasenko
We show integrality of instanton numbers in several key examples of mirror symmetry. Our methods are essentially elementary, they are based on our previous work in the series of pa…
Dwork crystals III: from excellent Frobenius lifts towards supercongruences
Frits Beukers, Masha Vlasenko
This paper is a continuation of our Dwork crystals series. Here we exploit the Cartier operation to prove supercongruences for expansion coefficients of rational functions. In the…