Arithmetic properties of Apéry-like numbers
نویسندگان
چکیده
منابع مشابه
Arithmetic Properties 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 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.
متن کاملCatalan and Apéry numbers in residue classes
We estimate character sums with Catalan numbers and middle binomial coefficients modulo a prime p. We use this bound to show that the first at most p13/2(log p)6 elements of each sequence already fall in all residue classes modulo every sufficiently large p, which improves the previously known result requiring pO(p) elements. We also study, using a different technique, similar questions for seq...
متن کاملArithmetic Properties of Generalized Euler Numbers
The generalized Euler number En|k counts the number of permutations of {1, 2, . . . , n} which have a descent in position m if and only if m is divisible by k. The classical Euler numbers are the special case when k = 2. In this paper, we study divisibility properties of a q-analog of En|k. In particular, we generalize two theorems of Andrews and Gessel [3] about factors of the q-tangent numbers.
متن کاملApéry Numbers and Central Trinomial Coefficients 3
Define the Apéry polynomial of degree n by A n (x) = n k=0 n k 2 n + k k 2. We determine p−1 k=0 (−1) k A k (1/4) and p−1 k=0 (−1) k A k (1/16) modulo a prime p > 3. Let b and c be integers and let the generalized trinomial coefficient T n (b, c) be the coefficient of x n in the expansion of (x 2 +bx+c) n. We establish the following new congruence p−1 k=0 T k (b, c) 2 (b 2 − 4c) k ≡ c(b 2 − 4c)...
متن کاملArithmetic properties of q-Fibonacci numbers and q-pell numbers
We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
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: Compositio Mathematica
سال: 2017
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x17007552