Fourier-Bohr spectrum of sequences related to continued fractions |
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| Authors: | Jean Coquet Georges Rhin Philippe Toffin |
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| Institution: | UER de Sciences exactes et naturelles, Département de mathématiques, Le Mont Houy 59326 Valenciennes-Cedex, France;Faculté des Sciences, Département de mathématiques et informatique, Ile du Saulcy, 57045 Metz Cedex, France;Université de Caen, Département de mathématiques et mécanique, Esplanade de la Paix, 14032 Caen Cedex, France |
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| Abstract: | Let α be a real irrational number and q1, q2, q3,… the sequence of denominators of the convergents of α. Call σα(n)) the sum of the digits of the integer n in basis q1, q2, q3,…. The Fourier-Bohr spectrum of the sequence exp(2πiσα(n)) and more generally of sequences exp(2πif(n)) is studied, where f is a completely α-additive real sequence. A sufficient condition is derived for the sequence xn + yσα(n) to be uniformly distributed modulo one. |
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