Elliptic curves and special values of Gaussian 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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Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of Fp points on algebraic varieties and to Fourier coefficients of modular forms. In this paper, we explicitly determine these functions modulo higher powers of p and discuss an application to super...
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Let p be an odd prime. The purpose of this paper is to refine methods of Ahlgren and Ono [2] and Kilbourn [13] in order to prove a general mod p congruence for the Gaussian hypergeometric series n+1Fn(λ) where n is an odd positive integer. As a result, we extend three recent supercongruences. The first is a result of Ono and Ahlgren [2] on a supercongruence for Apéry numbers which was conjectur...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.03.010