10 citations · 58 across the 28 of their papers we have counts for
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An asymptotic Robin inequality
Patrick Solé, Yuyang Zhu
The conjectured Robin inequality for an integer is where denotes Euler constant, and . Robin proved that this conjecture i…
Improving riemann prime counting
Michel Planat, Patrick Solé
Prime number theorem asserts that (at large ) the prime counting function is approximately the logarithmic integral $\mbox{li}(x)$. In the intermediate range, Riemann pri…
Chebyshev's bias and generalized Riemann hypothesis
Adel Alamadhi, Michel Planat, Patrick Solé
It is well known that (i) up to the (very large) Skewes' number \cite{Bays00}. But, according to a Littlewood's theorem, there exist in…
Efficient prime counting and the Chebyshev primes
Michel Planat, Patrick Solé
The function $ε(x)=\mbox{li}(x)-π(x)$ is known to be positive up to the (very large) Skewes' number. Besides, according to Robin's work, the functions $ε_θ(x)=\mbox{li}[θ(x)]-π(x)$…
On Nicolas criterion for the Riemann Hypothesis
Youngju Choie, Michel Planat, Patrick Solé
Nicolas criterion for the Riemann Hypothesis is based on an inequality that Euler totient function must satisfy at primorial numbers. A natural approach to derive this inequality w…
Robin inequality for free integers
Patrick Solé, Michel Planat
Recall that an integer is free iff it is not divisible by for some prime We give a method to check Robin inequality for free integers $n…