
Congruences for L-Functions
Springer (Publisher)
Published on 15. December 2010
Book
Paperback/Softback
XII, 256 pages
978-90-481-5490-6 (ISBN)
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
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 2000
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XII, 256 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
417 gr
ISBN-13
978-90-481-5490-6 (9789048154906)
DOI
10.1007/978-94-015-9542-1
Schweitzer Classification
Other editions
Additional editions

J. Urbanowicz | Kenneth S. Williams
Congruences for L-Functions
Book
06/2000
Kluwer Academic Publishers
€53.49
Shipment within 15-20 days
Content
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.