| Congruences for L-Functions 2000 Edition Contributor(s): Urbanowicz, J. (Author), Williams, Kenneth S. (Author) |
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ISBN: 0792363795 ISBN-13: 9780792363798 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: June 2000 Annotation: This book provides a comprehensive and up-to-date treatment of research carried out in the last twenty years on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. There is no other book on the market which deals with this subject. The book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to the recent ones of Gras, Vehara, and others. Audience: This book is aimed at graduate students and researchers interested in (analytic) number theory, functions of a complex variable and special functions. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Medical |
| Dewey: 512.74 |
| LCCN: 00033054 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.69" H x 6.14" W x 9.21" (1.24 lbs) 256 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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 |