Isbn: 9789048154906 - congruences for l-functions (mathematics and its applications, band 511) (4 Ergebnisse)

Zustand: New. In English.

Paperback. Zustand: Brand New. 272 pages. 9.00x6.00x0.62 inches. In Stock.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.…

Taschenbuch. Zustand: Neu. Congruences for L-Functions | J. Urbanowicz (u. a.) | Taschenbuch | xii | Englisch | 2010 | Springer | EAN 9789048154906 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. …