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AuthorMurty, M. Ram. author
TitleNon-vanishing of L-Functions and Applications [electronic resource] / by M. Ram Murty, V. Kumar Murty
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997
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Descript XI, 196 p. 2 illus. online resource


This monograph brings together a collection of results on the non-vanishing of Lยญ functions. The presentation, though based largely on the original papers, is suitable for independent study. A number of exercises have also been provided to aid in this endeavour. The exercises are of varying difficulty and those which require more effort have been marked with an asterisk. The authors would like to thank the Institut d'Estudis Catalans for their encouragement of this work through the Ferran Sunyer i Balaguer Prize. We would 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 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 distriยญ 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 theยญ 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

Mathematics Algebraic geometry Mathematics Algebraic Geometry


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