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arXiv:math/0311162math.NT

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.

arXiv comments
30 pages
Journal reference
DOI
Subjects
math.NTNumber Theory

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  1. How I learned to love and fear the Riemann Hypothesis 1 comment

    • There's been a lot of research that has assumed it to be true and built on top of it to find deeper implications. Still, a number of people who've worked most closely with the Riemann zeta function, even the ones who led the computations and numerical verifications, have…

      rfurmaniView on HNParent context

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