Special Values of the Hypergeometric Series
نویسندگان
چکیده
منابع مشابه
Values of Gaussian Hypergeometric Series
Let p be prime and let GF (p) be the finite field with p elements. In this note we investigate the arithmetic properties of the Gaussian hypergeometric functions 2F1(x) =2 F1 „ φ, φ | x « and 3F2(x) =3 F2 „ φ, φ, φ , | x « where φ and respectively are the quadratic and trivial characters of GF (p). For all but finitely many rational numbers x = λ, there exist two elliptic curves 2E1(λ) and 3E2(...
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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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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2017
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/1177