Number Theory

   

Convergence of the Riemann Z Function

Authors: Horacio Useche

The Riemann conjeture is false. The zeros of the function $zeta(s)$ are place on $0.43leq Re(s) < 1$ interval. The straight lines with possible infinite zeros are $Re(z)=0.43$, $Re(z)=0.47$, $Re(z)=0.55$, $Re(z)=0.67$, $Re(z)=0.79$, $Re(z)=0.84$, $Re(z)=0.90$, $Re(z)=0.91$, $Re(z)=0.92$, $Re(z)=0.93$, $Re(z)=0.94$, $Re(z)=0.95$, $Re(z)=0.96$, $Re(z)=0.97$, $Re(z)=0.98$, y $Re(z)=0.99$, there are other lines with many zeros, though with minor density.We provide necessary and sufficient conditions to yields the convergence of the zeros of the Riemann zeta ($zeta$) function. A new expression for the Riemann zeta function is also deduced, in terms of a serie of sines and cosines, as expected! In the same way, we confirm the existence of the textbf{zeros by reflection} predicted by the functional equation of the zeta function and we define the concept of textbf{twin zeros} by analogy with the twin primes of the numbers theory.

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[v1] 2025-08-09 03:17:18

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