Ebook: Pisot and Salem Numbers
- Tags: Number Theory
- Year: 1992
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xiii
Rational Series....Pages 1-18
Compact Families of Rational Functions....Pages 19-25
Meromorphic Functions on D(0,1). Generalized Schur Algorithm....Pages 27-60
Generalities Concerning Distribution Modulo 1 of Real Sequences....Pages 61-75
Pisot Numbers, Salem Numbers and Distribution Modulo 1....Pages 77-99
Limit Points of Pisot and Salem Sets....Pages 101-117
Small Pisot Numbers....Pages 119-151
Some Properties and Applications of Pisot Numbers....Pages 153-168
Algebraic Number Sets....Pages 169-176
Rational Functions Over Rings of Adeles....Pages 177-188
Generalizations of Pisot and Salem Numbers to Adeles....Pages 189-218
Pisot Elements in a Field of Formal Power Series....Pages 219-228
Pisot Sequences, Boyd Sequences and Linear Recurrence....Pages 229-260
Generalizations of Pisot and Boyd Sequences....Pages 261-270
The Salem-Zygmund Theorem....Pages 271-291
Content:
Front Matter....Pages i-xiii
Rational Series....Pages 1-18
Compact Families of Rational Functions....Pages 19-25
Meromorphic Functions on D(0,1). Generalized Schur Algorithm....Pages 27-60
Generalities Concerning Distribution Modulo 1 of Real Sequences....Pages 61-75
Pisot Numbers, Salem Numbers and Distribution Modulo 1....Pages 77-99
Limit Points of Pisot and Salem Sets....Pages 101-117
Small Pisot Numbers....Pages 119-151
Some Properties and Applications of Pisot Numbers....Pages 153-168
Algebraic Number Sets....Pages 169-176
Rational Functions Over Rings of Adeles....Pages 177-188
Generalizations of Pisot and Salem Numbers to Adeles....Pages 189-218
Pisot Elements in a Field of Formal Power Series....Pages 219-228
Pisot Sequences, Boyd Sequences and Linear Recurrence....Pages 229-260
Generalizations of Pisot and Boyd Sequences....Pages 261-270
The Salem-Zygmund Theorem....Pages 271-291
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