Authors: Yuri Heymann
In the present study we used the Dirichlet eta function as an extension of the Riemann zeta function in the strip Re(s) in ]0, 1[. We then determined the domain of admissible complex zeros of the Riemann zeta function in this strip using minimal constraints and alternative series of power functions. While proving the uniqueness of the line Re(s) = 1/2 in the strip Re(s) in ]0, 1[, we obtained the value of the Dirichlet eta function evaluated at the point s = 1/2 which was fortuitous. We also checked for zeros outside this strip. We found that the admissible domain of complex zeros excluding the trivial zeros is the critical line given by Re(s) = 1/2 as stated in the Riemann hypothesis.
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