Author | Bertin, M. J. author |
---|---|
Title | Pisot and Salem Numbers [electronic resource] / by M. J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse, J. P. Schreiber |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8632-1 |
Descript | XIII, 291 p. online resource |
1 Rational series -- 1.1 Algebraic criteria of rationality -- 1.2 Criteria of rationality in C -- 1.3 Generalized Fatouโs lemma -- Notes -- References -- 2 Compact families of rational functions -- 2.1 Properties of formal series with rational coefficients -- 2.2 Compact families of rational functions -- Notes -- References -- 3 Meromorphic functions on D(0,1). Generalized Schur algorithm -- 3.0 Notation -- 3.1 Properties of Schurโs determinants -- 3.2 Characterization of functions belonging to M -- 3.3 Generalized Schur algorithm -- 3.4 Characterization of certain meromorphic functions on D(0,1) -- 3.5 Smythโs theorem -- Notes -- References -- 4 Generalities concerning distribution modulo 1 of real sequences -- 4.0 Notation and examples -- 4.1 Sequences with finitely many limit points modulo 1 -- 4.2 Uniform distribution of sequences -- 4.3 Weylโs theorems -- 4.4 Van der Corputโs and Fejerโs theorems. Applications -- 4.5 Koksmaโs theorem -- 4.6 Some notions about uniform distribution modulo 1 in Rp -- Notes -- References -- 5 Pisot numbers, Salem numbers and distribution modulo 1 -- 5.0 Notation -- 5.1 Some sequences (??n) non-uniformly distributed modulo 1 -- 5.2 Pisot numbers and Salem numbers. Definitions and algebraic properties -- 5.3 Distribution modulo 1 of the sequences (?n) with ? a U-number -- 5.4 Pisot numbers and distribution modulo 1 of certain sequences (??n) -- 5.5 Salem numbers and distribution modulo 1 of certain sequences (??n) -- 5.6 Sequences (??n) non-uniformly distributed modulo 1 -- Notes -- References -- 6 Limit points of Pisot and Salem sets -- 6.0 Notation -- 6.1 Closure of the set S -- 6.2 The derived set S? of S -- 6.3 Successive derived sets of S -- 6.4 Limit points of the set T -- Notes -- References -- 7 Small Pisot numbers -- 7.1 Schurโs approximations for elements of N*1 -- 7.2 Small Pisot numbers -- 7.3 The smallest number of S? -- Notes -- References -- 8 Some properties and applications of Pisot numbers -- 8.1 Some algebraic properties and applications of Pisot and Salem numbers -- 8.2 An application of Pisot numbers to a problem of uniform distribution -- 8.3 Application of Pisot numbers to a problem of rational approximations of algebraic numbers -- 8.4 Pisot numbers and the Jacobi-Perron algorithm -- Notes -- References -- 9 Algebraic number sets -- 9.1 Sq sets -- 9.2 n-tuples of algebraic numbers -- Notes -- References -- 10 Rational functions over rings of adeles -- 10.1 Adeles of Q -- 10.2 Analytic functions in Cp -- 10.3 Rationality criteria in QI[[X]] -- 10.4 Compact families of rational functions -- Notes -- References -- 11 Generalizations of Pisot and Salem numbers to adeles -- 11.1 Definition of the set UI -- 11.2 Subsets of UI and characterizations -- 11.3 The sets SI? -- 11.4 The sets TI -- 11.5 The sets SIJ -- 11.6 The sets BI -- 11.7 Closed subsets of SI? -- 11.8 Limit points of the sets TI -- Notes -- References -- 12 Pisot elements in a field of formal power series -- 12.0 Generalities and notation -- 12.1 Definitions of the sets U and S -- 12.2 Characterizations of the sets U and S -- 12.3 Limit points of the sets U and S -- 12.4 Relation between the sets S and S -- Notes -- References -- 13 Pisot sequences, Boyd sequences and linear recurrence -- 13.0 Convergence theorems -- 13.1 Pisot sequences -- 13.2 Linear recurrence and Pisot sequences -- 13.3 Boyd sequences -- Notes -- References -- 14 Generalizations of Pisot and Boyd sequences -- 14.1 Convergence theorems in AI -- 14.2 Pisot sequences in AI -- 14.3 Boyd sequences in AI -- 14.4 Pisot and Boyd sequences in a field of formal power series -- Notes -- References -- l5 The Salem-Zygmund theorem -- 15.1 Introduction -- 15.2 Sets of uniqueness -- 15.3 Symmetric perfect sets -- 15.4 The sufficient condition for the Salem-Zygmund theorem -- 15.5 A theorem by Senge and Strauss -- References