Apéry numbers, Jacobi sums, and special values of generalizedp-adic hypergeometric functions

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Transcendence in Positive Characteristic and Special Values of Hypergeometric Functions

We prove a simple transcendence criterion suitable for function field arithmetic. We apply it to show the transcendence of special values at non-zero rational arguments (or more generally, at algebraic arguments which generate extension of the rational function field with less than q places at infinity) of the entire hypergeometric functions in the function field (over Fq) context, and to obtai...

متن کامل

Special Values of Hypergeometric Functions over Finite Fields

For an odd prime p, define Hp(z) = ∑ u,v(mod p) ( uv(1−u)(1−v)(1−uvz) p ) , where z is an integer (mod p) and the summands are Legendre symbols. The function Hp(z) was explicitly evaluated for z = 1 by Evans (1981) and for z = −1 by Greene and Stanton (1986). Koike (1992) determined Hp(1/4)(mod p), and Ono (1998) evaluated Hp(z) for z = 1/4,−1/8, and 1/64. This paper evaluates Hp(z) for infinit...

متن کامل

Special values of Kloosterman sums and binomial bent functions

Let p ≥ 7, q = p. Kq(a) = ∑ x∈Fpm ζ m 1 (x m−2+ax) is the Kloosterman sum of a on Fpm , where ζ = e 2π √ −1 p . The value 1− 2 ζ+ζ−1 of Kq(a) and its conjugate have close relationship with a class of binomial function with Dillon exponent. This paper first presents some necessary conditions for a such that Kq(a) = 1− 2 ζ+ζ−1 . Further, we prove that if p = 11, for any a, Kq(a) 6= 1− 2 ζ+ζ−1 . A...

متن کامل

SUMMATION IDENTITIES AND SPECIAL VALUES OF HYPERGEOMETRIC SERIES IN THE p-ADIC SETTING

We prove hypergeometric type summation identities for a function defined in terms of quotients of the p-adic gamma function by counting points on certain families of hyperelliptic curves over Fq . We also find certain special values of that function.

متن کامل

Hypergeometric Functions and Fibonacci Numbers

Hypergeometric functions are an important tool in many branches of pure and applied mathematics, and they encompass most special functions, including the Chebyshev polynomials. There are also well-known connections between Chebyshev polynomials and sequences of numbers and polynomials related to Fibonacci numbers. However, to my knowledge and with one small exception, direct connections between...

متن کامل

ذخیره 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: Journal of Number Theory

سال: 1992

ISSN: 0022-314X

DOI: 10.1016/0022-314x(92)90123-7