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Author | : |
Publisher | : Elsevier |
Total Pages | : 285 |
Release | : 2000-04-01 |
Genre | : Mathematics |
ISBN | : 008095412X |
Download Algebraic Numbers and Harmonic Analysis Book in PDF, ePub and Kindle
Algebraic Numbers and Harmonic Analysis
Author | : Yves Meyer |
Publisher | : |
Total Pages | : 274 |
Release | : 1972-01-01 |
Genre | : Algebraic number theory |
ISBN | : 9780720424522 |
Download Algebraic Numbers and Harmonic Analysis Book in PDF, ePub and Kindle
Diophantine approximations to real numbers. Some classical results in diophantine approximations. Measure-teoretical methods in diophantine approximations. Diophantine approximations and additive problems in locally compact abelian groups. Uniqueness of representation by trigonometric series. Problems on a-periodic trigonometric sums. Special trigonometric series (complex methods). Special trigonometric series (group-theoretic methods). Pisot numbers and spectral synthesis. Ultra-thin symmetric sets.
Author | : Raphael Salem |
Publisher | : |
Total Pages | : 98 |
Release | : 1983 |
Genre | : |
ISBN | : |
Download Algebraic Numbers and Fourier Analysis Book in PDF, ePub and Kindle
Author | : Raphaël Salem |
Publisher | : Wadsworth Company |
Total Pages | : 200 |
Release | : 1983 |
Genre | : Algebraic number theory |
ISBN | : |
Download Algebraic Numbers and Fourier Analysis Book in PDF, ePub and Kindle
Author | : Bruce Lyndon Aubertin |
Publisher | : |
Total Pages | : 250 |
Release | : 1986 |
Genre | : p-adic fields |
ISBN | : |
Download Algebraic Numbers and Harmonic Analysis in the P-series Case Book in PDF, ePub and Kindle
Author | : Dinakar Ramakrishnan |
Publisher | : Springer Science & Business Media |
Total Pages | : 372 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475730853 |
Download Fourier Analysis on Number Fields Book in PDF, ePub and Kindle
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.
Author | : Valentin Blomer |
Publisher | : Springer Science & Business Media |
Total Pages | : 301 |
Release | : 2011-11-19 |
Genre | : Mathematics |
ISBN | : 1461412196 |
Download Contributions in Analytic and Algebraic Number Theory Book in PDF, ePub and Kindle
The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.
Author | : Helmut Koch |
Publisher | : American Mathematical Soc. |
Total Pages | : 390 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821820544 |
Download Number Theory Book in PDF, ePub and Kindle
Algebraic number theory is one of the most refined creations in mathematics. It has been developed by some of the leading mathematicians of this and previous centuries. The primary goal of this book is to present the essential elements of algebraic number theory, including the theory of normal extensions up through a glimpse of class field theory. Following the example set for us by Kronecker, Weber, Hilbert and Artin, algebraic functions are handled here on an equal footing with algebraic numbers. This is done on the one hand to demonstrate the analogy between number fields and function fields, which is especially clear in the case where the ground field is a finite field. On the other hand, in this way one obtains an introduction to the theory of 'higher congruences' as an important element of 'arithmetic geometry'. Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem. There are a detailed exposition of the theory of Hecke $L$-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory. The book attempts as much as possible to give simple proofs. It can be used by a beginner in algebraic number theory who wishes to see some of the true power and depth of the subject. The book is suitable for two one-semester courses, with the first four chapters serving to develop the basic material. Chapters 6 through 9 could be used on their own as a second semester course.
Author | : Marie J. Bertin |
Publisher | : Birkhäuser |
Total Pages | : 297 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034886322 |
Download Pisot and Salem Numbers Book in PDF, ePub and Kindle
the attention of The publication of Charles Pisot's thesis in 1938 brought to the mathematical community those marvelous numbers now known as the Pisot numbers (or the Pisot-Vijayaraghavan numbers). Although these numbers had been discovered earlier by A. Thue and then by G. H. Hardy, it was Pisot's result in that paper of 1938 that provided the link to harmonic analysis, as discovered by Raphael Salem and described in a series of papers in the 1940s. In one of these papers, Salem introduced the related class of numbers, now universally known as the Salem numbers. These two sets of algebraic numbers are distinguished by some striking arith metic properties that account for their appearance in many diverse areas of mathematics: harmonic analysis, ergodic theory, dynamical systems and alge braic groups. Until now, the best known and most accessible introduction to these num bers has been the beautiful little monograph of Salem, Algebraic Numbers and Fourier Analysis, first published in 1963. Since the publication of Salem's book, however, there has been much progress in the study of these numbers. Pisot had long expressed the desire to publish an up-to-date account of this work, but his death in 1984 left this task unfulfilled.
Author | : Robert S. Doran, Paul J. Sally, Jr., and Loren Spice |
Publisher | : American Mathematical Soc. |
Total Pages | : 294 |
Release | : 2011 |
Genre | : Harmonic analysis |
ISBN | : 0821874039 |
Download Harmonic Analysis on Reductive, $p$-adic Groups Book in PDF, ePub and Kindle