On some reasons for doubting the Riemann hypothesis

Aleksandar Ivić

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On some reasons for doubting the Riemann hypothesis

Aleksandar Ivić

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Abstract

Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|ζ(1/2+it)|$ on the critical line, and zeros of a class of convolution functions. The first two topics are classical, and the remaining ones are connected with the author's research.

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BibTeX RIS

Aleksandar Ivić. 2003-11-11. On some reasons for doubting the Riemann hypothesis. https://arxiv.org/abs/math/0311162

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