Congruences for $\sb 3F\sb 2$ hypergeometric functions over finite fields
نویسندگان
چکیده
منابع مشابه
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...
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We prove a general identity for a 3F2 hypergeometric function over a finite field Fq, where q is a power of an odd prime. A special case of this identity was proved by Greene and Stanton in 1986. As an application, we prove a finite field analogue of Clausen’s Theorem expressing a 3F2 as the square of a 2F1. As another application, we evaluate an infinite family of 3F2(z) over Fq at z = −1/8. T...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2002
ISSN: 0019-2082
DOI: 10.1215/ijm/1258130978