Sur certaines \'equations fonctionnelles approch\'ees, li\'ees \`a la transformation de Gauss
Number Theory
2018-07-17 v1 Classical Analysis and ODEs
Abstract
In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence criterion for a diophantine series considered by Chowla, and to give additional information about the sum of this series.
Keywords
Cite
@article{arxiv.1807.05719,
title = {Sur certaines \'equations fonctionnelles approch\'ees, li\'ees \`a la transformation de Gauss},
author = {Michel Balazard and Bruno Martin},
journal= {arXiv preprint arXiv:1807.05719},
year = {2018}
}
Comments
in French. Aequationes Mathematicae, Springer Verlag, A para\^itre