The approximate functional equation of some Diophantine series

Fernando Chamizo; Bruno Martin

doi:10.1007/s00605-023-01859-6

The approximate functional equation of some Diophantine series

Mon Hefte Math. 2023;202(1):41-52. doi: 10.1007/s00605-023-01859-6. Epub 2023 May 5.

Authors

Fernando Chamizo^#¹, Bruno Martin^#²

Affiliations

¹ Department of Mathematics, Universidad Autónoma de Madrid and ICMAT, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain.
² Laboratoire de Mathématiques Pures et Appliquées, CNRS, Université du Littoral Côte d'Opale, 50 rue F. Buisson, BP 599, 62228 Calais Cedex, France.

^# Contributed equally.

Abstract

We prove that a family of Diophantine series satisfies an approximate functional equation. It generalizes a result by Rivoal and Roques and proves an extended version of a conjecture posed in their paper. We also characterize the convergence points.

Keywords: Approximate functional equation; Continuity; Convergence; Diophantine series.