论文标题
通过Mellin变换，功率系列和反射关系的Riemann假设
The Riemann hypothesis via the Mellin transform, power series and the reflection relations
论文作者
论文摘要
通过依靠梅林转化的特性，提出了Riemann假设的证明。函数$ \ mathfrak {g}_η\ left（t \ firt）$在集合的集合$ \ bar {\ mathbb {\ mathbb {r}} _+$的非阴性实际数字的特殊功率系列中，以某种方式，以某种方式，以至于Mellin Transform $ \ hat $ \ hat $ \ hat $ \ hat {\ mathfrak} \ s_ s s} $ \ mathfrak {g}_η\ left（t \ right）$在基本条中不会消失$ 0 <\ permatatorName {re} s <1/2 $。在此条中，riemann zeta函数的每个零零$ζ\ left（1-s \ right）$是函数$ \ hat {\ mathfrak {g}}}_η\ left（s \ right）$的零。因此，事实证明，riemann zeta函数$ζ\ left（s \ right）$中没有零零，$ 1/2 <\ permatatorName {re} s <1 $。反射关系围绕$ \ operatorname {re} s = 1/2 $ for $ s \ neq 0,1 $，证明Riemann zeta Zeta函数$ζ\ left（s \ right）$中没有零零。总之，事实证明，riemann zeta函数$ζ\ left（s \ right）$中没有零零，$ 0 <\ operatatorName {re} s <1 $ for $ \ operatatorName {re} re} s \ neq 1/2 $。
A proof of the Riemann hypothesis is proposed by relying on the properties of the Mellin transform. The function $\mathfrak{G}_η\left(t\right)$ 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 $\hat{\mathfrak{G}}_η\left(s\right)$ of the function $\mathfrak{G}_η\left(t\right)$ does not vanish in the fundamental strip $0<\operatorname{Re} s <1/2$. In this strip every zero of the Riemann zeta function $ζ\left(1-s\right)$ is a zero of the function $\hat{\mathfrak{G}}_η\left(s\right)$. Consequently, it is proved that no zero of the Riemann zeta function $ζ\left(s\right)$ exists in the strip $1/2<\operatorname{Re} s <1$. The reflection relations, which hold around the line $\operatorname{Re} s =1/2$ for $s\neq 0,1$, prove that no zero of the Riemann zeta function $ζ\left(s\right)$ exists in the strip $0<\operatorname{Re} s<1/2$. In conclusion, it is proved that no zero of the Riemann zeta function $ζ\left(s\right)$ exists in the strip $0<\operatorname{Re} s<1$ for $\operatorname{Re} s\neq 1/2$.
