Congruences for L-Functions (Hardcover, 2000 ed.)

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences proved previously by other authors using various means. The Hardy-Williams idea was as follows. Let d be the discriminant of a quadratic field. Suppose that d is odd and let d = PIP2* . . Pn be its unique decomposition into prime discriminants. Then, for any positive integer k coprime with d, the congruence holds trivially as each Legendre-Jacobi-Kronecker symbol (~) has the value + 1 or -1. Expanding this product gives ~ eld e:=l (mod4) where e runs through the positive and negative divisors of d and v (e) denotes the number of distinct prime factors of e. Summing this congruence for o < k < Idl/8, gcd(k, d) = 1, gives ~ (-It(e) ~ (~) =:O(mod2n). eld o

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 511
Release date:	2001
First published:	June 2000
Authors:	J. Urbanowicz • Kenneth S. Williams
Dimensions:	234 x 156 x 17mm (L x W x T)
Format:	Hardcover
Pages:	256
Edition:	2000 ed.
ISBN-13:	978-0-7923-6379-8
Categories:	Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	0-7923-6379-5
Barcode:	9780792363798

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