Supercongruences for Apéry-like Numbers
نویسندگان
چکیده
It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like differential equations.
منابع مشابه
Multivariate Apéry Numbers and Supercongruences of Rational Functions
One of the many remarkable properties of the Apéry numbers A(n), introduced in Apéry’s proof of the irrationality of ζ(3), is that they satisfy the two-term supercongruences A(pm) ≡ A(pr−1m) (mod p) for primes p > 5. Similar congruences are conjectured to hold for all Apéry-like sequences. We provide a fresh perspective on the supercongruences satisfied by the Apéry numbers by showing that they...
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It is known that the numbers which occur in Apéry’s proof of the irrationality of ζ(2) have many interesting congruences properties while the associated generating function satisfies a second order differential equation. We prove congruences for numbers which arise in Beukers’ and Zagier’s study of integral solutions of Apéry-like differential equations.
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تاریخ انتشار 2011