Moscow Mathematical Journal

Volume 15, Issue 4, October–December 2015 pp. 629–652.

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

Authors: Michel Balazard (1) and Bruno Martin (2)
Author institution:(1) Institut de Mathématiques de Marseille, CNRS, Université d’Aix-Marseille, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, FRANCE
(2) Laboratoire de Mathématiques Pures et Appliquées, CNRS, Université du Littoral Côte d’Opale, 50 rue F. Buisson, BP 599, 62228 Calais Cedex, FRANCE

Summary:

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.

2010 Math. Subj. Class. 11N37 (11L07).

Keywords: Approximate functional equations, divisor function, Mellin transform, Hilbert transform.

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