Patrick Solé

activity

20102026

F_{q} + v F_{q} + v^{2} F_{q}

10 citations · 58 across the 28 of their papers we have counts for

collaborators

Showing 2010Show all

5 papers · 1 filter

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-ph2010★ 9 cited

Riemann hypothesis and Quantum Mechanics

Michel Planat, Patrick Solé, Sami Omar

In their 1995 paper, Jean-Benoît Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function $ζ (β)$ , where $β$ is an inv…

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…

cs.IT2010

A Type II lattice of norm 8 in dimension 72

Jean-Claude Belfiore, Patrick Solé

A Type II lattice of norm 8 in dimension 72 is obtained by Construction A applied to an extended Quadratic Residue code over Z8. Its automorphism group contains a subgroup isomorph…

On Nicolas criterion for the Riemann Hypothesis

Robin inequality for 7−free integers

Riemann hypothesis and Quantum Mechanics

Extreme values of the Dedekind Ψ function

A Type II lattice of norm 8 in dimension 72

Robin inequality for $7 -$ free integers

Extreme values of the Dedekind $Ψ$ function