Zobrazeno 1 - 10
of 69
pro vyhledávání: '"Darses, Sébastien"'
Autor:
Darses, Sébastien, Najnudel, Joseph
We prove exact formulas for weighted $2k$th moments of the Riemann zeta function for all integer $k\geq 1$ in terms of the analytic continuation of an auto-correlation function. This latter enjoys several functional equations. One of them, following
Externí odkaz:
http://arxiv.org/abs/2311.02783
Autor:
Darses, Sébastien, Hillion, Erwan
We prove closed-form identities for the sequence of moments $\int t^{2n}|\Gamma(s)\zeta(s)|^2dt$ on the whole critical line $s=1/2+it$. They are finite sums involving binomial coefficients, Bernoulli numbers, Stirling numbers and $\pi$, especially fe
Externí odkaz:
http://arxiv.org/abs/2209.10990
The Nyman-Beurling criterion, equivalent to the Riemann hypothesis (RH), is an approximation problem in the space of square integrable functions on $(0,\infty)$, involving dilations of the fractional part function by factors $\theta_k\in(0,1)$, $k\ge
Externí odkaz:
http://arxiv.org/abs/2006.02953
Autor:
Darses, Sébastien, Hillion, Erwan
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 a reciprocity formula for cotangent sums, related to the ones proven i
Externí odkaz:
http://arxiv.org/abs/2004.10086
Akademický článek
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Autor:
Darses, Sébastien, Hillion, Erwan
The Nyman-Beurling criterion is an approximation problem in the space of square integrable functions on $(0,\infty)$, which is equivalent to the Riemann hypothesis. This involves dilations of the fractional part function by factors $\theta_k\in(0,1)$
Externí odkaz:
http://arxiv.org/abs/1805.06733
Autor:
Chretien, Stephane, Darses, Sebastien
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 and their role in physics, engineering and biology. In practice, real-wo
Externí odkaz:
http://arxiv.org/abs/1601.06042
Autor:
Chretien, Stephane, Darses, Sebastien
The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see \cite{BourgainTzafriri:IJM87,Tropp:StudiaMath08,Vershynin:IJM01} for
Externí odkaz:
http://arxiv.org/abs/1509.00748
Akademický článek
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Autor:
Chretien, Stephane, Darses, Sebastien
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal processing,
Externí odkaz:
http://arxiv.org/abs/1406.5441