Michel Balazard, Bruno Martin, “Sur une équation fonctionnelle approché due à J. R. Wilton”, Mosc. Math. J., 2015, Volume 15, Number 4,Pages <nobr>629

This article is cited in 2 papers

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

Michel Balazard^a, Bruno Martin^b

^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.

MSC: 11N37, 11L07

Received: January 16, 2015; in revised form August 4, 2015

Language: French

DOI: 10.17323/1609-4514-2015-15-4-629-652