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Suite de Rudin-Shapiro et modèle d’Ising. (Rudin-Shapiro sequence and Ising model). (French) Zbl 0592.10049

Let u(n) be the number of occurrences of 11 in the binary representation of the integer n. For every non-rational number x, the sequence x u(n) is proved to be uniformly distributed modulo 1. The proof is based upon a connection between a slightly modified Weyl sum for the sequence x u(n) and the partition function of the one-dimensional cyclic Ising model (used in statistical mechanics) for a purely imaginary temperature. The partition function is evaluated by means of the Kramers and Wannier method, and the modified Weyl sum and the real one are compared.
Reviewer: G.Christol

MSC:

11B83 Special sequences and polynomials
11J71 Distribution modulo one
11L99 Exponential sums and character sums
82-XX Statistical mechanics, structure of matter
42A05 Trigonometric polynomials, inequalities, extremal problems
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References:

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