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

2026/04/07 by Pedro Ribeiro · 1 voice
Mathematics · #math.HO

paper · pdf

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.

Citations

• Poisson summation formula and Index Transforms
• Generalizations (in the spirit of Koshliakov) of some formulas from Ramanujan's Lost Notebook
• Certain Extensions of Results of Siegel, Wilton and Hardy
• Two General Series Identities Involving Modified Bessel Functions and a Class of Arithmetical Functions
• On the Epstein zeta function and the zeros of a class of Dirichlet series
• Ramanujan and Koshliakov Meet Abel and Plana
• A Class of Identities Associated with Dirichlet Series Satisfying Hecke's Functional Equation
• Koshliakov zeta functions I: Modular Relations
• Sums of squares and products of Bessel functions
• On a theorem of A. I. Popov on sums of squares
• New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type
• Analogues of the general theta transformation formula
• Character analogues of Ramanujan type integrals involving the Riemann Ξ-function
• A transformation formula involving the Gamma and Riemann zeta functions in Ramanujan's Lost Notebook
• Zur Theorie allgemeiner Zetafunctionen
• Note sur les zéros de la fonction ζ(s) de Riemann

Discussions

• Pedro Ribeiro: Analogues of a formula of Ferrar: what I have learned from Semyon Yakubovich https://arxiv.org/abs/2604.09707 https://arxiv.org/pdf/2604.09707 https://arxiv.org/html/2604.09707 [bsky, 0 points, 0 comments]

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