On special values of generalized p-adic hypergeometric functions
نویسندگان
چکیده
منابع مشابه
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.
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Many authors have considered the problem of extending the Fibonacci sequence to arbitrary real or complex subscripts (cf. [1], [6], and references therein). Since the positive integers form a discrete subset of R the existence of multitudes of continuous functions f : R→ R such that f(n) = Fn for positive integers n is immediate and the question then becomes one of determining the various prope...
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We show that contrary to recent papers by S. Albeverio, A. Yu. Khrennikov and V. Shelkovich, point values do not determine elements of the so-called p-adic Colombeau-Egorov algebra G(Q p ) uniquely. We further show in a more general way that for an Egorov algebra G(M,R) of generalized functions on a locally compact ultrametric space (M, d) taking values in a nontrivial ring, a point value chara...
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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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Let G be a connected reductive algebraic group defined over a non-Archimedean local field F . The study of Whittaker functions on G has a long history. For example, if G = GL(2), an explicit formula for the Whittaker function is well-known (See [5]). Shintani proved an explicit formula for the case G = GL(n) and expressed it by Schur polynomials in [16]. Casselman and Shalika generalized Shinta...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1994
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-67-2-141-163