Conjectures in Arithmetic Algebraic Geometry: A Survey - Couverture souple

Hulsbergen, Wilfred W. J. W.J.

 
9783663095071: Conjectures in Arithmetic Algebraic Geometry: A Survey
Couverture souple
ISBN 10 : 366309507X ISBN 13 : 9783663095071
Editeur : Vieweg+Teubner Verlag, 2013

Synopsis

In this expository text we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued math- ematicians for a long period of time. Starting from Fermat's Last Theorem one is naturally led to introduce L- functions, the main, motivation being the calculation of class numbers. In partic- ular, Kummer showed that the class numbers of cyclotomic fields play a decisive role in the corroboration of Fermat's Last Theorem for a large class of exponents. Before Kummer, Dirichlet 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 properties of L-functions. Twentieth century number theory, class field theory and algebraic geome- try only strengthen the nineteenth century number theorists's view. We just mention the work of E. H cke, 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 generalization of Dirichlet's L-functions with a generalization of class field theory to non-abelian Galois extensions of number fields in mind.

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À propos de l?auteur

Dr. Wilfried Hulsbergen is teaching at the KMA, Breda, Niederlande.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Vieweg+Teubner Verlag
Date d'édition
2013
Langue
anglais
ISBN 10 
366309507X
ISBN 13 
9783663095071
Reliure
Broché
Numéro d'édition
2
Nombre de pages
256
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9783528164331: Conjectures in Arithmetic Algebraic Geometry: A Survey

Edition présentée

ISBN 10 :  3528164336 ISBN 13 :  9783528164331
Editeur : Friedrich Vieweg & Sohn Verl..., 1994
Couverture rigide