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A number theoretic estimate of Davenport from a functional analytic viewpoint

A number theoretic estimate of Davenport from a functional analytic viewpoint We consider the problem of the identification of continuous functionsf∶[0, 1]→R, by means of the sums\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sum\limits_{a = 1}^n {f\left( {\frac{a}{n}} \right)} $$\end{document}. This is not possible, in general, but we prove that it may be the case under auxiliary conditions. We also study the behaviour of a well known exceptional function. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

A number theoretic estimate of Davenport from a functional analytic viewpoint

Codeca, P.; Nair, M.
ANNALI DELL UNIVERSITA DI FERRARA , Volume 45 (1) – Jan 1, 1999
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Publisher
Springer Journals
Copyright
Copyright © Università degli Studi di Ferrara 1999
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/bf02826085
Publisher site
See Article on Publisher Site

Abstract

We consider the problem of the identification of continuous functionsf∶[0, 1]→R, by means of the sums\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\sum\limits_{a = 1}^n {f\left( {\frac{a}{n}} \right)} $$\end{document}. This is not possible, in general, but we prove that it may be the case under auxiliary conditions. We also study the behaviour of a well known exceptional function.

Journal

ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals

Published: Jan 1, 1999

Keywords: 26A15; 42A16; 11M06

References

  • Some special trigonometric series related to the distribution of prime numbers
    Bateman, P. T.; Chowla, S.
  • Problem on continuity
    Besicovitch, A. S.
  • Two problems related to the non vanishing of L(1,χ)
    Codecà, P.; Dvornicich, R.; Zannier, U.
  • On some infinite series involving arithmetical functions (II)
    Davenport, H.