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

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 $\Re (s)\in ]0,1[$ 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 $\bar{s}$ its complex conjugate, if $s$ is a zero of the Riemann zeta function in the critical strip $\Re (s)\in ]0,1[$, then $\zeta (s)=\zeta (1-\bar{s})$, as a key proposition to prove the Riemann hypothesis.

13 pages

Cited by in corpus (1)

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