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HARMONIC ANALYSIS ON THE POSITIVE RATIONALS. DETERMINATION OF THE GROUP GENERATED BY THE RATIOS $(an+b)/(An+B)$

Part of: Multiplicative number theory Probabilistic theory: distribution modulo $1$; metric theory of algorithms Exponential sums and character sums Abelian groups

Published online by Cambridge University Press:  29 November 2017

P. D. T. A. Elliott  and
Jonathan Kish
P. D. T. A. Elliott
Affiliation:
Department of Mathematics, University of Colorado Boulder, Boulder, Colorado 80309-0395, U.S.A. email pdtae@euclid.colorado.edu
Jonathan Kish
Affiliation:
Department of Applied Mathematics, University of Colorado Boulder, Boulder, Colorado 80309-0526, U.S.A. email jonathan.kish@colorado.edu
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Abstract

The multiplicative group generated by a certain sequence of rationals is determined, settling a 30-year conjecture.

MSC classification

Primary: 11K65: Arithmetic functions 11K70: Harmonic analysis and almost periodicity 11K99: None of the above, but in this section 20K99: None of the above, but in this section 11L05: Gauss and Kloosterman sums; generalizations 11L99: None of the above, but in this section 11N64: Other results on the distribution of values or the characterization of arithmetic functions 11N99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 63 , Issue 3 , 2017 , pp. 919 - 943
Copyright
Copyright © University College London 2017 

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