Analogues of a formula of Ferrar: what I have learned from Semyon Yakubovich

TL;DR

This paper explores generalizations of Ferrar's summation formulas, highlighting the role of the Mellin transform and insights gained from Semyon Yakubovich in understanding the connection between summation formulas and Dirichlet series.

Contribution

It introduces new generalizations of Ferrar's formulas and discusses their derivation through the Mellin transform, influenced by Semyon Yakubovich's work.

Findings

New generalizations of Ferrar's formulas are presented.

The Mellin transform links summation formulas to Dirichlet series.

Insights from Yakubovich influenced the development of these formulas.

Abstract

W. L. Ferrar seems to have been the first mathematician to clearly draw a connection between the functional aspects of a summation formula and the behavior of the Dirichlet series underlying it. Taking a formula due to him as a starting point, I will describe some new generalizations of Ferrar's formulas and how these were actually obtained after learning a great deal from Semyon. I also present a very concise overview of the underlying theory of summation formulas and how the Mellin transform has been the link between mine and Professor Yakubovich's interests.