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Item Details
| Title:
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CONGRUENCES FOR L-FUNCTIONS
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| By: |
Jerzy Urbanowicz, Kenneth S. Williams |
| Format: |
Hardback |
| List price:
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£71.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0792363795 |
| ISBN 13: |
9780792363798 |
| Publisher: |
SPRINGER |
| Pub. date: |
1 June, 2000 |
| Edition: |
2000 ed. |
| Series: |
Mathematics and Its Applications 511 |
| Pages: |
256 |
| Description: |
Provides a comprehensive treatment of research carried out on congruences involving the values of L-functions (attached to quadratic characters) at certain special values. This book presents in a unified way congruences found by many authors over the years, from the classical ones of Gauss and Dirichlet to Gras and Vehara. |
| Synopsis: |
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 |
| Illustrations: |
XII, 256 p. |
| Publication: |
Netherlands |
| Imprint: |
Springer |
| Returns: |
Returnable |
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