Congruences for L-functions
著者
書誌事項
Congruences for L-functions
（Mathematics and its applications, v. 511）
Kluwer Academic, c2000
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
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
目次
Preface. 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). Bibliography. Author Index. Subject Index. List of symbols.
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