Synopses & Reviews
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 volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.
About the Author
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.
Table of Contents
Preface.- Introduction.- Chapter 1 The Prime Number Theorem and Generalizations.- Chapter 2 Artin L-functions.- Chapter 3 Equidistribution and L-functions.- Chapter 4 Modular Forms and Dirichlet Series.- Chapter 5 Dirichlet L-functions.- Chapter 6 Non-vanishing of Quadratic Twists of Modular L-functions.- Chapter 7 Selberg's Conjectures.- Chapter 8 Suggestions for further reading.- Author index.- Subject index.