<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper the periodic even functions for which all the regular Riemann sums vanishe are called special periodic even functions. A construction of some of them is put forward, this one rest on the Fourier serie and H. Davenport’s estimations concerning the Moebius function. The special periodic even functions seem linked to the number theory, as this can be seen on the Fourier serie result, on the proposed constructions and on the proof that such functions cannot belong to the Wiener algebra.</p></abstract>

In this paper the periodic even functions for which all the regular Riemann sums vanishe are called special periodic even functions. A construction of some of them is put forward, this one rest on the Fourier serie and H. Davenport’s estimations concerning the Moebius function. The special periodic even functions seem linked to the number theory, as this can be seen on the Fourier serie result, on the proposed constructions and on the proof that such functions cannot belong to the Wiener algebra.

Special Periodic Even Functions

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

(Les Fonctions Périodiques Paires Spéciales)

In this paper the periodic even functions for which all the regular Riemann sums vanishe are called special periodic even functions. A construction of some of...

Special Periodic Even Functions

Published Online: Feb 01, 2019

Page range: 17 - 32

Received: Nov 07, 2018

Accepted: Dec 15, 2018

DOI: https://doi.org/10.1515/mjpaa-2018-0003

Keywords
éries de Fourier, fonctions de Moebius et de Liouville, estimation de H. Davenport

© 2018 Marcel Grangé, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Special Periodic Even Functions

Published Online: Feb 01, 2019

Page range: 17 - 32

Received: Nov 07, 2018

Accepted: Dec 15, 2018

DOI: https://doi.org/10.1515/mjpaa-2018-0003

Keywordséries de Fourier, fonctions de Moebius et de Liouville, estimation de H. Davenport

© 2018 Marcel Grangé, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
éries de Fourier, fonctions de Moebius et de Liouville, estimation de H. Davenport