An investigation of the non-trivial zeros of the Riemann zeta function

2018/04/04 by Yuri Heymann, Heymann, Yuri
Mathematics · Physics and Astronomy · #11M06 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1804.04700

openalex publication_date 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While many zeros of the Riemann zeta function are located on the critical line \Re(s)=1/2, the non-existence of zeros in the remaining part of the critical strip \Re(s) ∈ ]0, 1[ is the main scope to be proven for the Riemann hypothesis. The Riemann zeta functional leads to a relation between the zeros on either sides of the critical line. Given s a complex number and s its complex conjugate, if s is a zero of the Riemann zeta function in the critical strip \Re(s) ∈ ]0, 1[, then ζ(s) = ζ(1-s), as a key proposition to prove the Riemann hypothesis.

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