Del i serien New Mathematical Monographs

The Selberg Class of L-Functions

Inbunden, Engelska, 2027

2 339 kr

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The study of L-functions has become a major theme in modern number theory. The Selberg class arose as an attempt to capture the properties of L-functions, encouraging the study of properties of the class rather than of individual functions. Written by two experts in the field, this book surveys the current state of knowledge of the theory of the Selberg class of L-functions. It synthesises a large body of research spanning decades and presents a complete account of the classification of small-degree L-functions. The text covers numerous important developments, including the theory of nonlinear twists of L-functions, culminating in the application of these twists to converse theorems, moments of L-functions and the structure of local Euler factors. Proofs are streamlined and unified. Basic problems and conjectures have been included to stimulate further research. This will be a valuable resource for researchers, graduate students and advanced undergraduates in analytic number theory.

Produktinformation

Utgivningsdatum2027-02-28
FormatInbunden
SpråkEngelska
SerieNew Mathematical Monographs
Antal sidor350
FörlagCambridge University Press
ISBN9781047777810

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Algebra inom Naturvetenskap och teknik
Talteori inom Naturvetenskap och teknik

Jerzy Kaczorowski is a professor in the Faculty of Mathematics and Computer Science at Adam Mickiewicz University. Since 1996, he has been the Editor-in-Chief of Acta Arithmetica. He is a full member of the Polish Academy of Sciences and the Polish Academy of Arts and Sciences. He has authored around 120 research papers and specialises in analytic number theory. Alberto Perelli is a professor in the Department of Mathematics at the University of Genoa. He is the author of around 140 research papers and specialises in analytic number theory.

Introduction; Notation; 1. Basic theory of the Selberg class; 2. Classical 𝐿-functions and the Selberg class; 3. Invariants; 4. The standard twist; 5. Nonlinear twists with K0 ≤ 1/; 6. Auxiliary results from complex analysis; 7. Nonlinear twists with K0 > 1/; 8. Converse theorems; 9. Further applications of nonlinear twists; Appendix A. Dirichlet series; Appendix B. Almost periodic functions; Appendix C. Complex analysis; Appendix D. Some useful identities and inequalities; Appendix E. Additive semigroups of finite type; References; Symbol index; Subject index.