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" Congruences for L-Functions "
by Jerzy Urbanowicz, Kenneth S. Williams.
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BL
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| Record Number
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579203
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b408422
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| Main Entry
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Urbanowicz, Jerzy.
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| Title & Author
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Congruences for L-Functions\ by Jerzy Urbanowicz, Kenneth S. Williams.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 2000.
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| Series Statement
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Mathematics and Its Applications ;; 511
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| ISBN
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9789401595421
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: 9789048154906
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| Contents
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I. Short Character Sums -- II. Class Number Congruences -- III. Congruences between the Orders of K2-Groups -- IV Congruences among the Values of 2-Adic L-Functions -- V. Applications of Zagier's Formula (I) -- VI. Applications of Zagier's Formula (II) -- Author Index -- List of symbols.
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| Abstract
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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
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Mathematics.
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Field theory (Physics).
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Functions of complex variables.
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Functions, special.
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Number theory.
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| Added Entry
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Williams, Kenneth S.
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SpringerLink (Online service)
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