M. Planat

activity

20022023

most citedMutually Unbiased Bases and Finite Projective Planes

84 citations · 970 across the 84 of their papers we have counts for

collaborators

Showing 2010 · math.NTShow all

3 papers · 2 filters

math.NT2010★ 1 cited

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…

math.NT2010

Robin inequality for $7 -$ free integers

Patrick Solé, Michel Planat

Recall that an integer is $t -$ free iff it is not divisible by $p^{t}$ for some prime $p .$ We give a method to check Robin inequality $σ (n) < e^{γ} n lo g lo g n,$ for $t -$ free integers $n…

math.NT2010

Extreme values of the Dedekind $Ψ$ function

Patrick Solé, Michel Planat

Let $Ψ (n) := n \prod_{p ∣ n} (1 + \frac{1}{p})$ denote the Dedekind $Ψ$ function. Define, for $n \geq 3,$ the ratio $R (n) := \frac{Ψ ( n )}{n l o g l o g n} .$ We prove unconditionally that $R(n)< e…

On Nicolas criterion for the Riemann Hypothesis

Robin inequality for 7−free integers

Extreme values of the Dedekind Ψ function

Robin inequality for $7 -$ free integers

Extreme values of the Dedekind $Ψ$ function