EXTENDING GAUSSIAN HYPERGEOMETRIC SERIES TO THE p-ADIC SETTING
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.
متن کاملGaussian Hypergeometric series and supercongruences
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...
متن کاملValues 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(...
متن کاملp-ADIC INTERPOLATION OF THE FIBONACCI SEQUENCE VIA HYPERGEOMETRIC FUNCTIONS
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...
متن کاملGaussian Hypergeometric Series and Combinatorial Congruences
In a recent paper [A-O], the author and K. Ono study the “Gaussian” hypergeometric series 4F3(1)p over the finite field Fp. They describe relationships between values of these series, Fourier coefficients of modular forms, and the arithmetic of a certain algebraic variety. These relationships, together with tools from p-adic analysis and some unexpected combinatorial identities, lead to the pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2012
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042112500844