Julien Lange

Mobile spectral laws for compressed prime-power translations

We study the sum of zero-extended translations by logarithms of prime powers on L²([-a,a]), weighted by the von Mangoldt function divided by the square root. Its canonical mean spectral measure, after division by a, converges to the limiting mean measure of a Hermitian random Toe...

Mobile spectral laws for compressed prime-power translations

We study the sum of zero-extended translations by logarithms of prime powers on L²([-a,a]), weighted by the von Mangoldt function divided by the square root. Its canonical mean spectral measure, after division by a, converges to the limiting mean measure of a Hermitian random Toe...

The compression defect of a discrete-sine Galerkin section: an exact reflection identity, a window-truncation law, and two certification traps

Finite Galerkin certificates for the Weil quadratic form lose information in two independent ways: through what is discarded outside the band, and through the failure of the compression to be multiplicative inside it. The first loss was given an exact order theory by Groskin. Thi...

The compression defect of a discrete-sine Galerkin section: an exact reflection identity, a window-truncation law, and two certification traps

Finite Galerkin certificates for the Weil quadratic form lose information in two independent ways: through what is discarded outside the band, and through the failure of the compression to be multiplicative inside it. The first loss was given an exact order theory by Groskin. Thi...

Certified positivity of a Toeplitz–Cayley matrix family at the linear threshold a=3N

Version 2.0 gives a reproducible computer-assisted positivity proof for an explicit full Toeplitz–Cayley matrix family derived from the logarithmic derivative of the completed Riemann xi function. Writing Xi(q)=xi(1/2+q), h=Xi'/Xi, and defining the Toeplitz coefficients by sum_{n...