Fourier Analysis and Zeta Functions on Local Fields
Title | Fourier Analysis and Zeta Functions on Local Fields PDF eBook |
Author | Catriona Glenton |
Publisher | |
Pages | 192 |
Release | 1978 |
Genre | Functions, Zeta |
ISBN |
Fourier Analysis on Number Fields
Title | Fourier Analysis on Number Fields PDF eBook |
Author | Dinakar Ramakrishnan |
Publisher | Springer Science & Business Media |
Pages | 372 |
Release | 2013-04-17 |
Genre | Mathematics |
ISBN | 1475730853 |
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
Fourier Analysis on Local Fields. (MN-15)
Title | Fourier Analysis on Local Fields. (MN-15) PDF eBook |
Author | M. H. Taibleson |
Publisher | Princeton University Press |
Pages | 308 |
Release | 2015-03-08 |
Genre | Mathematics |
ISBN | 1400871336 |
This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Fourier Analysis in Number Fields and Hecke's Zeta-functions
Title | Fourier Analysis in Number Fields and Hecke's Zeta-functions PDF eBook |
Author | John Torrence Tate |
Publisher | |
Pages | 0 |
Release | 1950 |
Genre | Algebraic fields |
ISBN |
Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces
Title | Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces PDF eBook |
Author | Nicole Bopp |
Publisher | American Mathematical Soc. |
Pages | 250 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821836234 |
Intends to prove a functional equation for a local zeta function attached to the minimal spherical series for a class of real reductive symmetric spaces.
An Introduction to the Theory of Local Zeta Functions
Title | An Introduction to the Theory of Local Zeta Functions PDF eBook |
Author | Jun-ichi Igusa |
Publisher | American Mathematical Soc. |
Pages | 246 |
Release | 2000 |
Genre | Mathematics |
ISBN | 0821829076 |
This book is an introductory presentation to the theory of local zeta functions. Viewed as distributions, and mostly in the archimedean case, local zeta functions are also called complex powers. The volume contains major results on analytic and algebraic properties of complex powers by Atiyah, Bernstein, I. M. Gelfand, S. I. Gelfand, and Sato. Chapters devoted to $p$-adic local zeta functions present Serre's structure theorem, a rationality theorem, and many examples found by the author. The presentation concludes with theorems by Denef and Meuser. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Quaternion Algebras
Title | Quaternion Algebras PDF eBook |
Author | John Voight |
Publisher | Springer Nature |
Pages | 877 |
Release | 2021-06-28 |
Genre | Mathematics |
ISBN | 3030566943 |
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.