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 2010Show all

9 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…

quant-ph2010

About the Dedekind psi function in Pauli graphs

Michel R. P. Planat

We study the commutation structure within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$ , containing a square, into its factors. The simplest i…

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…

math.GM2010★ 5 cited

Riemann hypothesis from the Dedekind psi function

Michel Planat

Let $P$ be the set of all primes and $ψ (n) = n \prod_{n \in P, p ∣ n} (1 + 1/ p)$ be the Dedekind psi function. We show that the Riemann hypothesis is satisfied if and onl…