Congruences for L-Functions (Paperback, Softcover reprint of hardcover 1st ed. 2000)

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:	December 2010
First published:	2000
Authors:	J. Urbanowicz • Kenneth S. Williams
Dimensions:	240 x 160 x 14mm (L x W x T)
Format:	Paperback
Pages:	256
Edition:	Softcover reprint of hardcover 1st ed. 2000
ISBN-13:	978-90-481-5490-6
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Number theory > General
LSN:	90-481-5490-1
Barcode:	9789048154906

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