/sci/ - Science & Math

>>11661637
https://arxiv.org/pdf/2005.05741.pdf
>The Riemann hypothesis via the Mellin transform, power series and the reflection relations
>Filippo Giraldi

>A proof of the Riemann hypothesis is proposed by relying on the properties of the Mellin transform. The function Gη(t) is defined on the set R¯+ of the non-negative real numbers, in term of a special power series, in such a way that the Mellin transform G^η(s) of the function Gη(t) does not vanish in the fundamental strip 0<Res<1/2. In this strip every zero of the Riemann zeta function ζ(1−s) is a zero of the function G^η(s). Consequently, it is proved that no zero of the Riemann zeta function ζ(s) exists in the strip 1/2<Res<1. The reflection relations, which hold around the line Res=1/2 for s≠0,1, prove that no zero of the Riemann zeta function ζ(s) exists in the strip 0<Res<1/2. In conclusion, it is proved that no zero of the Riemann zeta function ζ(s) exists in the strip 0<Res<1 for Res≠1/2.