Congruences for L-Functions

ISBN-13: 9780792363798 / Angielski / Twarda / 2000 / 256 str.

Kenneth S. Williams; J. Urbanowicz; K. Williams

Opis

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

Spis treści

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.