9781466501928: Lectures on N Xp
Couverture rigide
ISBN 10 : 1466501928 ISBN 13 : 9781466501928
Editeur : A K Peters, 2011

Synopsis

Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in a context that is appealing to specialists in number theory and algebraic geometry.

Along with covering open problems, the text examines the size and congruence properties of NX(p) and describes the ways in which it is computed, by closed formulae and/or using efficient computers.

The first four chapters cover the preliminaries and contain almost no proofs. After an overview of the main theorems on NX(p), the book offers simple, illustrative examples and discusses the Chebotarev density theorem, which is essential in studying frobenian functions and frobenian sets. It also reviews ℓ-adic cohomology.

The author goes on to present results on group representations that are often difficult to find in the literature, such as the technique of computing Haar measures in a compact ℓ-adic group by performing a similar computation in a real compact Lie group. These results are then used to discuss the possible relations between two different families of equations X and Y. The author also describes the Archimedean properties of NX(p), a topic on which much less is known than in the ℓ-adic case. Following a chapter on the Sato-Tate conjecture and its concrete aspects, the book concludes with an account of the prime number theorem and the Chebotarev density theorem in higher dimensions.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Jean-Pierre Serre

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

Éditeur
A K Peters
Date d'édition
2011
Langue
anglais
ISBN 10 
1466501928
ISBN 13 
9781466501928
Reliure
Relié
Numéro d'édition
1
Nombre de pages
174
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9781032929088: Lectures on N_X(p)

Edition présentée

ISBN 10 :  1032929081 ISBN 13 :  9781032929088
Editeur : A K Peters/CRC Press, 2024
Couverture souple