Product details:
| ISBN13: | 9780792363798 |
| ISBN10: | 0792363795 |
| Binding: | Hardback |
| No. of pages: | 256 pages |
| Size: | 234x156 mm |
| Weight: | 1250 g |
| Language: | English |
| Illustrations: | XII, 256 p. |
| 0 |
Category:
Congruences for L-Functions
Series:
Mathematics and Its Applications;
511;
Edition number: 2000
Publisher: Springer
Date of Publication: 30 June 2000
Number of Volumes: 1 pieces, Book
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Long description:
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
Table of Contents:
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.
