Regularization for zeta functions with physical applications II

2007/02/03 by Minoru Fujimoto, Fujimoto, Minoru, Kunihiko Uehara +1
Mathematics · Physics and Astronomy · #11M06 #11M26 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math-ph/0702011

openalex publication_date 2007/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have proposed a regularization technique and apply it to the Euler product of zeta functions in the part one. In this paper that is the second part of the trilogy, we give another evidence to demonstrate the Riemann hypotheses by using the approximate functional equation. Some other results on the critical line are also presented using the relations between the Euler product and the deformed summation representions in the critical strip. In part three, we will focus on physical applications using these outcomes.

Citations

• Integral moments of L-functions

Related

• Regularization for zeta functions with physical applications I
• Regularizations of the Euler product representation for zeta functions and the Birch--Swinnerton-Dyer conjecture
• Regularized Euler product for the zeta function and the Birch and Swinnerton-Dyer and the Beilinson conjecture
• Analysis of the Riemann zeta function
• Finite Euler products and the Riemann Hypothesis