Rational Functions Over Rings of Adeles

M. J. Bertin, A. Decomps-Guilloux, M. Grandet-Hugot, M. Pathiaux-Delefosse and J. P. Schreiber
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M. J. Bertin: Université Pierre et Marie Curie Mathématiques
A. Decomps-Guilloux: Université Pierre et Marie Curie Mathématiques
M. Grandet-Hugot: Université de Caen Mathématiques
M. Pathiaux-Delefosse: Université Pierre et Marie Curie Mathématiques
J. P. Schreiber: Université d’Orléans, Château de la Source

Chapter Chapter 10 in Pisot and Salem Numbers, 1992, pp 177-188 from Springer

Abstract: Abstract In Chapter 11 we will discuss various generalizations of Pisot and Salem numbers. We will define sets with properties analogous to those of S and T, such as distribution modulo 1, or topological properties such as the fact that S is closed. The first attempt at generalization was to consider not algebraic integers but algebraic numbers that are zeros of polynomials in Z[X] and whose leading coefficient is a fixed integer q. These sets were discussed in Chapter 9. In fact, generalizing the distribution modulo 1 leads us to consider a more general framework: not the ring of adeles of Q, but certain subrings that provide an appropriate domain for such investigations through the Artin decomposition.

Date: 1992
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DOI: 10.1007/978-3-0348-8632-1_10

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