In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
EUR 3,19 für den Versand innerhalb von/der Deutschland
Versandziele, Kosten & DauerGratis für den Versand innerhalb von/der Deutschland
Versandziele, Kosten & DauerAnbieter: moluna, Greven, Deutschland
Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 1 The zero-dimensional case: number fields.- 1.1 Class Numbers.- 1.2 Dirichlet L-Functions.- 1.3 The Class Number Formula.- 1.4 Abelian Number Fields.- 1.5 Non-abelian Number Fields and Artin L-Functions.- 2 The one-dimensional case: elliptic curves.- 2.1 G. Bestandsnummer des Verkäufers 458647907
Anzahl: Mehr als 20 verfügbar
Anbieter: Buchmarie, Darmstadt, Deutschland
Zustand: Good. Cover Ecke leicht beschädigt. Bestandsnummer des Verkäufers 3514795_e68_3x
Anzahl: 1 verfügbar
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory. Bestandsnummer des Verkäufers 9783528064334
Anzahl: 1 verfügbar
Anbieter: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Deutschland
Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory. 240 pp. Deutsch. Bestandsnummer des Verkäufers 9783528064334
Anzahl: 2 verfügbar
Anbieter: buchversandmimpf2000, Emtmannsberg, BAYE, Deutschland
Taschenbuch. Zustand: Neu. Neuware -In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemann's paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theorists's view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlet's L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlet's L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory.Springer Vieweg in Springer Science + Business Media, Abraham-Lincoln-Straße 46, 65189 Wiesbaden 252 pp. Englisch. Bestandsnummer des Verkäufers 9783528064334
Anzahl: 2 verfügbar
Anbieter: Jackson Street Booksellers, Omaha, NE, USA
Hardcover. Zustand: Fine. No Jacket. 1st Edition. Fine in Hardcover. 236pp 8vo. Bestandsnummer des Verkäufers 162939
Anzahl: 1 verfügbar
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes Königreich
Zustand: New. In. Bestandsnummer des Verkäufers ria9783528064334_new
Anzahl: Mehr als 20 verfügbar
Anbieter: Chiron Media, Wallingford, Vereinigtes Königreich
PF. Zustand: New. Bestandsnummer des Verkäufers 6666-IUK-9783528064334
Anzahl: 10 verfügbar
Anbieter: California Books, Miami, FL, USA
Zustand: New. Bestandsnummer des Verkäufers I-9783528064334
Anzahl: Mehr als 20 verfügbar
Anbieter: Book Bear, West Brookfield, MA, USA
Hardcover. Zustand: Very Good. Zustand des Schutzumschlags: No Dust Jacket. 236 pp. Tightly bound. Tip of top right corner front board with light bump. Text is free of markings. No ownership markings. No dust jacket. Printed boards. Bestandsnummer des Verkäufers 031483
Anzahl: 1 verfügbar