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. --------- This book has been awarded the Ferran Sunyer I Balaguer 1996 prize (โฆ)The deepest results are contained in Chapter 6 on quadratic twists of modular L-functions with connections to the Birch-Swinnerton-Dyer conjecture. (โฆ) [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) ย Each chapter is accompanied by exercices, and there is a fair amount of introductory material, general discussion and recommended reading. (โฆ) it will be a useful addition to the library of any serious worker in this area. (Mathematical Reviews) ย (โฆ) 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)
CONTENT
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 Selbergโs Conjectures -- 8 Suggestions for Further Reading
