Dualities for absolute zeta functions and multiple gamma functions

2013/04/09 by Nobushige Kurokawa, Kurokawa, Nobushige, Hiroyuki Ochiai +1
Mathematics · #11M06 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.1304.2472

arxiv created 2013/04/09 · openalex publication_date 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study absolute zeta functions from the view point of a canonical normalization. We introduce the absolute Hurwitz zeta function for the normalization. In particular, we show that the theory of multiple gamma and sine functions gives good normalizations in cases related to the Kurokawa tensor product. In these cases, the functional equation of the absolute zeta function turns out to be equivalent to the simplicity of the associated non-classical multiple sine function of negative degree.

Citations

• Characteristic one, entropy and the absolute point

Related

• Bilateral zeta functions associated with the multiple sine functions
• Bilateral zeta functions and their applications
• Gamma,Psi,Bernoulli Functions via Hurwitz Zeta Function
• On gamma functions with respect to the alternating Hurwitz zeta functions
• Instant Multiple Zeta Values at Non-Positive Integers and Bernoulli Functions