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Diophantine Approximation and Dirichlet Series
Hervé Queffélec and Martine Queffélec, Université de Lille 1, Villeneuve d'Ascq, France
A publication of Hindustan Book Agency.
cover
Hindustan Book Agency
2013; 244 pp; softcover
ISBN-13: 978-93-80250-53-3
List Price: US$52
Member Price: US$41.60
Order Code: HIN/63
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This self-contained book is intended to be read with profit by beginners as well as researchers. It is devoted to Diophantine approximation, the analytic theory of Dirichlet series, and some connections between these two domains, which often occur through the Kronecker approximation theorem. Accordingly, the book is divided into seven chapters, the first three of which present tools from commutative harmonic analysis, including a sharp form of the uncertainty principle, ergodic theory and Diophantine approximation to be used in the sequel. A presentation of continued fraction expansions, including the mixing property of the Gauss map, is given.

Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of analytic functions in a half-plane. Finally, chapter seven presents the Bagchi-Voronin universality theorems, for the zeta function, and \(r\)-tuples of \(L\)-functions. The proofs, which mix hilbertian geometry, complex and harmonic analysis, and ergodic theory, are a very good illustration of the material studied earlier.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Researchers interested in number theory with an emphasis on Diophantine approximation and the anyalytic theory of Dirichlet series.

Table of Contents

  • A review of commutative harmonic analysis
  • Ergodic theory and Kronecker's theorems
  • Diophantine approximation
  • General properties of Dirichlet series
  • Probabilistic methods for Dirichlet series
  • Hardy spaces of Dirichlet series
  • Voronin type theorems
  • Index
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