On some reasons for doubting the Riemann hypothesis

2003/11/11 by Aleksandar Ivić, Ivić, Aleksandar · 7 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical Dynamics and Fractals #math.NT #msc:11M06

paper · pdf · doi:10.48550/arxiv.math/0311162

30 pages

arxiv created 2003/11/11 · arxiv updated 2009/12/01

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.

Citations

• Sur la distribution des nombres premiers

Cited by

• Note on Prime Gaps and Zero Spacings
• Lehmer pairs and binomial series
• Moments of Hardy's function over short intervals
• Inequalities For The Primes Counting Function
• An extension to the complex plane of the Riemann-Siegel Z function
• Simple Zeros Of The Zeta Function
• Lower bound for the maximum of some derivative of Hardy's function

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