Buch, Englisch, 189 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 312 g
Buch, Englisch, 189 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 312 g
ISBN: 978-90-481-6168-3
Verlag: Springer Netherlands
The Lerch zeta-function is the first monograph on this topic, which is a generalization of the classic Riemann, and Hurwitz zeta-functions. Although analytic results have been presented previously in various monographs on zeta-functions, this is the first book containing both analytic and probability theory of Lerch zeta-functions.
The book starts with classical analytical theory (Euler gamma-functions, functional equation, mean square). The majority of the presented results are new: on approximate functional equations and its applications and on zero distribution (zero-free regions, number of nontrivial zeros etc). Special attention is given to limit theorems in the sense of the weak convergence of probability measures for the Lerch zeta-function. From limit theorems in the space of analytic functions the universitality and functional independence is derived. In this respect the book continues the research of the first author presented in the monograph
This book will be useful to researchers and graduate students working in analytic and probabilistic number theory, and can also be used as a textbook for postgraduate students.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
Weitere Infos & Material
Preface.- 1: Euler Gamma-Function.- 2: Functional Equation.- 3: Moments.- 4: Approximate Functional Equation.- 5: Statistical Properties.- 6: Universality.- 7: Functional Independence.- 8: Distribution of Zeros.- References.- Notation.- Subject Index.
