Supercongruences and complex multiplication
نویسندگان
چکیده
منابع مشابه
Complex Multiplication
These are preliminary notes 1 for a modern account of the theory of complex multiplication. A shortened (minimal) version will be included in my book on Shimura varieties, and a complete longer version may one day be published separately. Please send comments and corrections to me at [email protected]. 1 This should be taken seriously: there are omissions, repetitions, clumsy statements and proof...
متن کاملComplex Multiplication
Class field theory describes the abelian extensions of a number field using the arithmetic of that field. The Kronecker-Weber theorem states that all abelian extensions of the rationals are contained in cyclotomic fields. As we know, cyclotomic fields can be generated by special values of the exponential function e, and we call this the theory of complex multiplication for Gm. We would thus lik...
متن کاملLegendre polynomials and supercongruences
Let p > 3 be a prime, and let Rp be the set of rational numbers whose denominator is not divisible by p. Let {Pn(x)} be the Legendre polynomials. In this paper we mainly show that for m,n, t ∈ Rp with m 6≡ 0 (mod p), P[ p 6 ](t) ≡ − (3 p ) p−1 ∑ x=0 (x3 − 3x + 2t p ) (mod p)
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 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: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.12.013