2010, ISBN: 9789048154906

[ED: Softcover], [PU: Springer / Springer Netherlands], In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of ima… Meer...

[ED: Softcover], [PU: Springer / Springer Netherlands], 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 2010. xii, 256 S. XII, 256 p. 240 mm Versandfertig in 6-10 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Offene Rechnung (Vorkasse vorbehalten)<

2010, ISBN: 9789048154906

[ED: Softcover], [PU: Springer Netherlands], In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quad… Meer...

[ED: Softcover], [PU: Springer Netherlands], 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 2010. xii, 256 S. 240 mm Versandfertig in 6-10 Tagen, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Offene Rechnung (Vorkasse vorbehalten)<

ISBN: 9789048154906

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. The… Meer...

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 Mathematics Soft cover, Springer Shop<

2010, ISBN: 9789048154906

pocketboek

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In [Hardy and Williams, 1986] t… Meer...

[ED: Kartoniert / Broschiert], [PU: Springer Netherlands], Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modul, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Taschenbuch, 256, [GW: 386g], 1. Auflage, Banküberweisung, PayPal, [CT: Naturwissenschaft/Mathematik / Sonstiges - Naturwissenschaften]<

2010, ISBN: 9789048154906

Buch, Softcover, Softcover reprint of hardcover 1st ed. 2000, [PU: Springer], Springer, 2010