On some reasons for doubting the Riemann hypothesis

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 $|\zeta (1/2+it)|$ 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.

30 pages

Cited by in corpus (9)

• Will a physicist prove the Riemann Hypothesis?
• Notes on the Riemann Hypothesis
• Note on Prime Gaps and Zero Spacings
• Lower bound for the maximum of some derivative of Hardy's function
• Inequalities For The Primes Counting Function
• An extension to the complex plane of the Riemann-Siegel Z function
• Simple Zeros Of The Zeta Function
• On some relations for Mellin transforms of Hardy's function
• Moments of Hardy's function over short intervals