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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 629–652 (Mi mmj578)  

Sur une équation fonctionnelle approché due à J. R. Wilton

Michel Balazarda, Bruno Martinb

a Institut de Mathématiques de Marseille, CNRS, Université d'Aix-Marseille, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, FRANCE
b Laboratoire de Mathématiques Pures et Appliquées, CNRS, Université du Littoral Côte d'Opale, 50 rue F. Buisson, BP 599, 62228 Calais Cedex, FRANCE

Abstract: We give a new proof of an approximate functional equation, due to J. R. Wilton, for a trigonometric sum involving the divisor function. This allows us to improve on Wilton's error term and to give an explicit formula for an unspecified function involved in the functional equation.

Key words and phrases: approximate functional equations, divisor function, Mellin transform, Hilbert transform.

DOI: https://doi.org/10.17323/1609-4514-2015-15-4-629-652

Full text: http://www.mathjournals.org/.../2015-015-004-004.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 11N37, 11L07
Received: January 16, 2015; in revised form August 4, 2015
Language:

Citation: Michel Balazard, Bruno Martin, “Sur une équation fonctionnelle approché due à J. R. Wilton”, Mosc. Math. J., 15:4 (2015), 629–652

Citation in format AMSBIB
\Bibitem{BalMar15}
\by Michel~Balazard, Bruno~Martin
\paper Sur une \'equation fonctionnelle approch\'e due \`a~J.\,R.~Wilton
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 629--652
\mathnet{http://mi.mathnet.ru/mmj578}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-629-652}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438825}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000368530900004}


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