منابع مشابه
Supercongruences for Sporadic Sequences
We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.
متن کاملSupercongruences for Apéry-like Numbers
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.
متن کاملRamanujan-type Supercongruences
We present several supercongruences that may be viewed as p-adic analogues of Ramanujan-type series for 1/π and 1/π 2 , and prove three of these examples.
متن کامل“divergent” Ramanujan-type Supercongruences
“Divergent” Ramanujan-type series for 1/π and 1/π2 provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to prove three of the supercongruences by means of the Wilf–Zeilberger algorithmic technique.
متن کاملLegendre polynomials and supercongruences
Let p > 3 be a prime, and let Rp be the set of rational numbers whose denominator is not divisible by p. Let {Pn(x)} be the Legendre polynomials. In this paper we mainly show that for m,n, t ∈ Rp with m 6≡ 0 (mod p), P[ p 6 ](t) ≡ − (3 p ) p−1 ∑ x=0 (x3 − 3x + 2t p ) (mod p)
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2015
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091515000255