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.

M. J Bertin; A Decomps-Guilloux; M Grandet-Hugot; M Pathiaux-Delefosse; J. P Schreiber

Marie José Bertin; A. Decomps-Guilloux

None; Bertin, Marie José

Basel ; Boston: Birkhäuser Verlag

Birkhäuser Boston

Birkhäuser GmbH

Birkhauser

Springer

United States, United States of America

Basel, Boston, Switzerland, 1992

Basel, cop. 1992

Germany, Germany

1, 1992

1993

Includes bibliographical references.

ix, 291 pages : 25 cm
Includes bibliographical references
Rational series -- Compact families of rational functions -- Meromorphic functions on D(0,1), generalized Schur algorithm -- Generalities concerning distribution modulo 1 of real sequences -- Pisot numbers, Salem numbers, and distribution modulo 1 -- Limit points of Pisot and Salem sets -- Small Pisot numbers -- Some properties and applications of Pisot numbers -- Algebraic number sets -- Rational functions over rings of adeles -- Generalizations of Pisot and Salem numbers to adeles -- Pisot elements in a field of formal power series -- Pisot sequences, Boyd sequences and linear recurrence -- Generalizations of Pisot and Boyd sequences -- The Salem-Zygmund theorem

2023-06-28