10 citations · 23 across the 14 of their papers we have counts for
18 papers
Weighted mean squares of and : closed forms, reciprocity, and a missing identity
Sébastien Darses, Erwan Hillion
This short note is a concise yet complete overview, intended for students, researchers, and AIs, bringing together in a unified notation the closed-form and reciprocity identities…
Polynomial Moments with a weighted Zeta Square measure on the critical line
Sébastien Darses, Erwan Hillion
We prove closed-form identities for the sequence of moments on the whole critical line . They are finite sums involving binomial coefficients,…
Polynomial approximations in a generalized Nyman-Beurling criterion
François Alouges, Sébastien Darses, Erwan Hillion
The Nyman-Beurling criterion, equivalent to the Riemann hypothesis (RH), is an approximation problem in the space of square integrable functions on , involving dilation…
An exponentially averaged Vasyunin formula
Sébastien Darses, Erwan Hillion
We prove a Vasyunin-type formula for an autocorrelation function arising from a Nyman-Beurling criterion generalized to a probabilistic framework. This formula can also be seen as…
On probabilistic generalizations of the Nyman-Beurling criterion for the zeta function
Sébastien Darses, Erwan Hillion
The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on , which is equivalent to the Riemann hypothesis. This involves d…
Controllability of complex networks using perturbation theory of extreme singular values
Stephane Chretien, Sebastien Darses
Pinning control on complex dynamical networks has emerged as a very important topic in recent trends of control theory due to the extensive study of collective coupled behaviors an…