Variations on criteria of Pólya and Turán for the Riemann hypothesis
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DOI: 10.1016/j.jnt.2021.01.004
Abstract: Abstract For 0 ≤ α ≤ 1 , let L α ( x ) = ∑ n ≤ x λ ( n ) n α , where λ ( n ) is the Liouville function.… read more here.
Keywords: hypothesis; riemann hypothesis; sign; quasi riemann ... See more keywords
p-adic Wan-Riemann hypothesis for Zp-towers of curves
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DOI: 10.1016/j.jpaa.2021.106743
Abstract: Abstract Our goal in this paper is to investigate four conjectures, proposed by Daqing Wan, about the stable behavior of a geometric Z p -tower of curves X ∞ / X . Let h n… read more here.
Keywords: riemann hypothesis; wan riemann; adic wan;
A New Reason for Doubting the Riemann Hypothesis
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DOI: 10.1080/10586458.2019.1586600
Abstract: We make plausible the existence of counterexamples to the Riemann hypothesis located in the neighbourhood of unusually large peaks of $\vert \zeta \vert$. The main ingredient in our argument is an identity which links the… read more here.
Keywords: reason doubting; new reason; doubting riemann; riemann hypothesis ... See more keywords
Generalized Riemann hypothesis, time series and normal distributions
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DOI: 10.1088/1742-5468/aaf717
Abstract: $L$ functions based on Dirichlet characters are natural generalizations of the Riemann $\zeta(s)$ function: they both have series representations and satisfy an Euler product representation, i.e. an infinite product taken over prime numbers. In this… read more here.
Keywords: time series; dirichlet; product; series ... See more keywords
Analogues of the Robin–Lagarias criteria for the Riemann hypothesis
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DOI: 10.1142/s1793042121500111
Abstract: Robin's criterion states that the Riemann hypothesis is equivalent to $\sigma(n) < e^\gamma n \log\log n$ for all integers $n \geq 5041$, where $\sigma(n)$ is the sum of divisors of $n$ and $\gamma$ is the… read more here.
Keywords: hypothesis equivalent; analogues robin; sigma; riemann hypothesis ... See more keywords