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pro vyhledávání: '"Hillion, Erwan"'
Extending results of Harg{\'e} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov$_\mu(f, g)$ where $\mu$ is a general product probability measure on $\mathbb{R}^d$ and $f,g: \mathbb{R}^d \to \mathbb{R}$ satisfy some convex
Externí odkaz:
http://arxiv.org/abs/2302.05208
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
Autor:
Bonnefont, Michel1 michel.bonnefont@math.u-bordeaux.fr, Hillion, Erwan2 erwan.hillion@univ-amu.fr, Saumard, Adrien3 adrien.saumard@ensai.fr
Publikováno v:
ALEA. Latin American Journal of Probability & Mathematical Statistics. 2024, Vol. 21 Issue 1, p627-660. 34p.
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2022 Jan 01. 34(3), 767-785.
Externí odkaz:
https://www.jstor.org/stable/48712091
Autor:
Hillion, Erwan, Johnson, Oliver
Publikováno v:
Electronic Journal of Probability, vol 24/126, 2019, pages 1-14
Consider tossing a collection of coins, each fair or biased towards heads, and take the distribution of the total number of heads that result. It is natural to conjecture that this distribution should be 'more random' when each coin is fairer. Indeed
Externí odkaz:
http://arxiv.org/abs/1810.09791
Publikováno v:
Statistics and Probability Letters, vol 145, 2019, pages 181-186
We prove, using the Brascamp-Lieb inequality, that the Gaussian measure is the only strong log-concave measure having a strong log-concavity parameter equal to its covariance matrix. We also give a similar characterization of the Poisson measure in t
Externí odkaz:
http://arxiv.org/abs/1806.05577
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
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