Some series representing the zeta function for <inline-formula><tex-math id="M1"> \Re(s)&gt;1 </tex-math></inline-formula>

2026/01/01 by Jean-François Burnol
Computer Science · Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT #semigroups and automata theory

paper · pdf · doi:10.3934/fcnt.2026023

openalex publication_date 2026/01/01 · openalex created_date 2026/07/28 · openalex updated_date 2026/07/30

Abstract

We represent the Riemann zeta function in the half-plane \Re s &gt;1 via series whose terms admit geometrically decreasing bounds. This is based upon simple combinatorics of certain measures, and their associated moments, which are defined on words from an alphabet of digits in a given radix b .

Citations

• Analytical study of the pantograph equation using Jacobi theta functions
• Dirichlet series of integers with missing digits
• Combinatorics on words and generating Dirichlet series of automatic sequences

Related

• Geometry of the Riemann Zeta Function
• Strategies To Evaluate The Riemann Zeta Function
• Series representation of the Riemann zeta function and other results:\n Complements to a paper of Crandall
• A New Series Representation Involving Root Of Unity For The Values Of Riemann Zeta Function At Integer Arguments
• Bounding zeta on the 1-line under the partial Riemann hypothesis