Non-vanishing of L-Functions and Applications: Modern Birkhäuser Classics

1 The Prime Number Theorem and Generalizations.- 2 Artin L-Functions.- 3 Equidistribution and L-Functions.- 4 Modular Forms and Dirichlet Series.- 5 Dirichlet L-Functions.- 6 Non-Vanishing of Quadratic Twists of Modular L-Functions.- 7 Selberg’s Conjectures.- 8 Suggestions for Further Reading.

From the book reviews:
“This is the softcover reprint of a monograph that was awarded the Ferran Sunyer i Balaguer prize in 1996. It is devoted to a recurring theme in number theory, namely that the non-vanishing of L-functions implies important arithmetical results. … Giving a well-informed overview of related results it will continue to be an important source of information for graduate students and researchers … .” (Ch. Baxa, Monatshefte für Mathematik, 2014)

M. Ram Murty is a Professor of Mathematics at the Queen's University in Kingston, ON, Canada.
V. Kumar Murty is a Professor of Mathematics at the University of Toronto.

This book systematically develops some methods for proving the non-vanishing of certain L-functions at points in the critical strip. Researchers in number theory, graduate students who wish to enter into the area and non-specialists who wish to acquire an introduction to the subject will benefit by a study of this book. One of the most attractive features of the monograph is that it begins at a very basic level and quickly develops enough aspects of the theory to bring the reader to a point where the latest discoveries as are presented in the final chapters can be fully appreciated.
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This book has been awarded the Ferran Sunyer I Balaguer 1996 prize (…)The deepest results are contained in Chapter 6 on quadratic twists of modular L-functions with connections to the Birch-Swinnerton-Dyer conjecture. (…) [It] is well-suited and stimulating for the graduate level because there is a wealth of recent results and open problems, and also a number of exercices and references after each chapter.
(Zentralblatt MATH)
 
Each chapter is accompanied by exercices, and there is a fair amount of introductory material, general discussion and recommended reading. (…) it will be a useful addition to the library of any serious worker in this area.
(Mathematical Reviews)
 
(…) well written monograph, intended not only for researchers and graduate students specializing in number theory, but also for non-specialists desiring to acquire an introduction to this difficult but very attractive and beautiful domain of investigation.
(Mathematica)

Well-written monograph on a difficult but attractive subject in number theory Provides an excellent easy-to-read introduction to the modern analytic theory of L-functions Each chapter is accompanied by exercises ? Includes supplementary material: sn.pub/extras