I. F. Avdeev
Abstract
A new proof of Ingam’s theorem on the density of zeros of the Riemann zeta-function in the critical strip is given basing on an idea of H. Bohr and F. Carlson. Multiplication of segments of the Dirichlet series for the functions ζ ( s ) and 1/ ζ ( s ) is used, which permits to simplify the proof.
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A new proof of Ingam’s theorem on the density of zeros of the Riemann zeta-function in the critical strip is given basing on an idea of H. Bohr and F. Carlson. Multiplication of segments of the Dirichlet series for the functions ζ ( s ) and 1/ ζ ( s ) is used, which permits to simplify the proof.
Key concepts: Mathematics, Riemann zeta function, Riemann hypothesis, Dirichlet series, Dirichlet eta function, Explicit formulae, Dirichlet distribution, Pure mathematics