Non-vanishing of L-Functions and Applications

Beschreibung

Neuware -This monograph brings together a collection of results on the non-vanishing of- functions.Thepresentation,thoughbasedlargelyontheoriginalpapers,issuitable forindependentstudy.Anumberofexerciseshavealsobeenprovidedtoaidinthis endeavour. The exercises are of varying di culty and those which require more e ort have been marked with an asterisk. The authors would like to thank the Institut d¿Estudis Catalans for their encouragementof thiswork throughtheFerranSunyeriBalaguerPrize.Wewould also like to thank the Institute for Advanced Study, Princeton for the excellent conditions which made this work possible, as well as NSERC, NSF and FCAR for funding. Princeton M. Ram Murty August, 1996 V. Kumar Murty xi Introduction Since the time of Dirichlet and Riemann, the analytic properties of L-functions have been used to establish theorems of a purely arithmetic nature. The dist- bution of prime numbers in arithmetic progressions is intimately connected with non-vanishing properties of various L-functions. With the subsequent advent of the Tauberian theory as developed by Wiener and Ikehara, these arithmetical t- orems have been shown to be equivalent to the non-vanishing of these L-functions on the line Re(s)=1. In the 1950¿s, a new theme was introduced by Birch and Swinnerton-Dyer. Given an elliptic curve E over a number eld K of nite degree over Q,they associated an L-function to E and conjectured that this L-function extends to an entire function and has a zero at s = 1 of order equal to the Z-rank of the group of K-rational points of E. In particular, the L-function vanishes at s=1ifand only if E has in nitely many K-rational points.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 208 pp. Englisch.

Bestandsnummer des Verkäufers 9783034802734

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Bibliografische Details

Titel

Non-vanishing of L-Functions and Applications

Verlag

Springer Basel, Springer Basel Jan 2012

Erscheinungsjahr

2012

Sprache

Englisch

ISBN-10

3034802730

ISBN-13

9783034802734

Einband

Taschenbuch

Zustand

Neu

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