منابع مشابه
ON p-ADIC FUNCTIONAL INTEGRATION
p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude Kv(x, t′′; x′, t′) (v = ∞, 2, 3, · · · , p, · · ·) for a particle in a constant field is calculated. Path integrals over Qp have the same form as those over R.
متن کاملON p-ADIC GENERALIZED WHITTAKER FUNCTIONS ON GSp(4)
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...
متن کاملp-ADIC CONGRUENCES FOR GENERALIZED FIBONACCI SEQUENCES
is the ordinary formal power series generating function for the sequence {yn+i}„>0 (cf. [12]. Furthermore, it is easy to see [1] that when the discriminant A = X +4ju ofP(t) is nonnegative and X & 0, the ratios yn+l I yn converge (in the usual archimedean metric on U) to a reciprocal root a of P(t). In this article we show that ratios of these y n also exhibit rapid convergence properties relat...
متن کاملGENERALIZED SPHERICAL FUNCTIONS ON REDUCTIVE p-ADIC GROUPS
Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...
متن کاملINTEGRATION ON p-ADIC GROUPS AND CRYSTAL BASES
Let G = GLr+1 over a nonarchimedean local field F . The Kashiwara crystal B(∞) is the quantized enveloping algebra of the lower triangular maximal unipotent subgroup N−. Examples are given where an integral over N−(F ) may be replaced by a sum over B(∞). Thus the Gindikin-Karpelevich formula evaluates the integral of the standard spherical vector in the induced model of a principal series repre...
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ژورنال
عنوان ژورنال: Mémoires de la Société mathématique de France
سال: 1974
ISSN: 0249-633X,2275-3230
DOI: 10.24033/msmf.175