An Analytic Proof of the Riemann Hypothesis
نویسنده
چکیده
Using the ζ functional equation and the Hadamard product, an analytical expression for the sum of the reciprocal of the ζ zeros is established. We then demonstrate that on the critical line, |ζ| is convex, and that in the region 0 < <(s) ≤ 0.5, |ζ| has a negative slope. In each case, analytical formulae are established, and numerical examples are presented to validate these formulae.
منابع مشابه
On an analytic estimate in the theory of the Riemann zeta function and a theorem of Báez-Duarte.
On the Riemann hypothesis we establish a uniform upper estimate for zeta(s)/zeta (s + A), 0 < or = A, on the critical line. We use this to give a purely complex-analytic variant of Báez-Duarte's proof of a strengthened Nyman-Beurling criterion for the validity of the Riemann Hypothesis. We investigate function-theoretically some of the functions defined by Báez-Duarte in his study and we show t...
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