Michel Planat

collaborators

4 papers

math.NT2026

Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements

Michel Planat

We study the de Bruijn--Newman family $H_{τ} (z)$ , with heat-deformation parameter $τ$ and $H_{0} (z) = \frac{1}{8}, ξ (\frac{1}{2} + \frac{i z}{2})$ . The moving zeros considered here are therefore…

math.NT2026

Morse Topology, Zero Products, and Elliptic Prime Crossings

Michel Planat

We study how the noncentral zeros of an elliptic-curve $L$ -function enter the Birch--Swinnerton-Dyer (BSD) leading coefficient and the prime-scale crossings of an elliptic Chebyshe…

math.CV2026

Second-Level Concavity of the Riemann $Ξ$ Kernel

Michel Planat, Patrick Solé

Let $Φ$ be the classical Jacobi-theta kernel in the Fourier representation of the Riemann $Ξ$ -function, set $s (t) = Φ (t)$ , and define the first Laguerre expression $f(t)=s'(t)^…

math-ph2026

Symmetry-Fixed Holonomies and Spectral Isolation in Two-Cycle Photonic Geometries A Square Parent Manifold for a Qubit and a Hexagonal Qutrit Manifold

Michel Planat

A system with two periodic directions carries two commuting holonomies $a=(u,v)\in\R^2/\Z^2$. We determine their distinguished values while separating lattice, arithmetic, and ob…

Collective Contraction in the de Bruijn--Newman Heat Flow: Off-Zero Logarithmic Derivatives and Certified Barrier Refinements

Morse Topology, Zero Products, and Elliptic Prime Crossings

Second-Level Concavity of the Riemann Ξ Kernel

Symmetry-Fixed Holonomies and Spectral Isolation in Two-Cycle Photonic Geometries A Square Parent Manifold for a Qubit and a Hexagonal Qutrit Manifold

Second-Level Concavity of the Riemann $Ξ$ Kernel