Congruences for L-Functions
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Book Overview
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
Format:Paperback
Language:English
ISBN:9048154901
ISBN13:9789048154906
Release Date:December 2010
Publisher:Springer
Length:256 Pages
Weight:0.85 lbs.
Dimensions:0.6" x 6.1" x 9.2"
Related Subjects
Algebra & Trigonometry General Geometry Math Mathematics Medical Medical Books Medicine Science & MathCustomer Reviews
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