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• W3025930188 abstract "A proof of the Riemann hypothesis is proposed by relying on the properties of the Mellin transform. The function $mathfrak{G}_{eta}left(tright)$ is defined on the set $bar{mathbb{R}}_+$ of the non-negative real numbers, in term of a special power series, in such a way that the Mellin transform $hat{mathfrak{G}}_{eta}left(sright)$ of the function $mathfrak{G}_{eta}left(tright)$ does not vanish in the fundamental strip $0<operatorname{Re} s <1/2$. In this strip every zero of the Riemann zeta function $zetaleft(1-sright)$ is a zero of the function $hat{mathfrak{G}}_{eta}left(sright)$. Consequently, it is proved that no zero of the Riemann zeta function $zetaleft(sright)$ exists in the strip $1/2<operatorname{Re} s <1$. The reflection relations, which hold around the line $operatorname{Re} s =1/2$ for $sneq 0,1$, prove that no zero of the Riemann zeta function $zetaleft(sright)$ exists in the strip $0<operatorname{Re} s<1/2$. In conclusion, it is proved that no zero of the Riemann zeta function $zetaleft(sright)$ exists in the strip $0<operatorname{Re} s<1$ for $operatorname{Re} sneq 1/2$." @default.
• W3025930188 created "2020-05-21" @default.
• W3025930188 creator A5046596094 @default.
• W3025930188 date "2020-05-11" @default.
• W3025930188 modified "2023-09-27" @default.
• W3025930188 title "The Riemann hypothesis via the Mellin transform, power series and the reflection relations" @default.
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