Zobrazeno 1 - 10
of 190
pro vyhledávání: '"Paulin, Frédéric"'
Autor:
Parkkonen, Jouni, Paulin, Frédéric
Let $A^-$ and $A^+$ be properly immersed closed locally convex subsets of a Riemannian manifold $M$ with pinched negative sectional curvature. When the Bowen-Margulis measure on $T^1M$ is finite and mixing for the geodesic flow, we prove that the Leb
Externí odkaz:
http://arxiv.org/abs/2410.09216
Autor:
Parkkonen, Jouni, Paulin, Frédéric
We give an asymptotic formula as $t\to+\infty$ for the number of common perpendiculars of length at most $t$ between two divergent geodesics or a divergent geodesic and a compact locally convex subset in negatively curved locally symmetric spaces wit
Externí odkaz:
http://arxiv.org/abs/2409.18251
Autor:
Horesh, Tal, Paulin, Frédéric
Let $\nu$ be a place of a global function field $K$ over a finite field, with associated affine function ring $R_\nu$ and completion $K_\nu$, and let $1 \leq \mathfrak{m}<\textbf{d}$. The aim of this paper is to prove an effective triple joint equidi
Externí odkaz:
http://arxiv.org/abs/2404.04368
Autor:
Parkkonen, Jouni, Paulin, Frédéric
Publikováno v:
Ergod. Th. Dynam. Sys. 44 (2024) 2700-2736
We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial e
Externí odkaz:
http://arxiv.org/abs/2212.09123
Autor:
Parkkonen, Jouni, Paulin, Frédéric
We study the correlations of pairs of complex logarithms of $\mathbb Z$-lattice points in the complex line at various scalings, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations exhibit le
Externí odkaz:
http://arxiv.org/abs/2206.14600
Autor:
Parkkonen, Jouni, Paulin, Frédéric
We extend formulae of Mertens and Mirsky on the asymptotic behaviour of the standard Euler function to the Euler functions of principal rings of integers of imaginary quadratic number fields, giving versions in angular sector and with congruences.
Externí odkaz:
http://arxiv.org/abs/2205.15844
Autor:
Parkkonen, Jouni, Paulin, Frédéric
We prove an abstract result on the correlations of pairs of elements in an exponentially growing discrete subset $\mathcal E$ of $[0,+\infty[\,$ endowed with a weight function. Assume that there exist $\alpha\in\mathbb R$, $c,\delta>0$ such that, as
Externí odkaz:
http://arxiv.org/abs/2201.12118
In this paper, we study inhomogeneous Diophantine approximation over the completion $K_v$ of a global function field $K$ (over a finite field) for a discrete valuation $v$, with affine algebra $R_v$. We obtain an effective upper bound for the Hausdor
Externí odkaz:
http://arxiv.org/abs/2112.04144
Autor:
Parkkonen, Jouni, Paulin, Frédéric
Publikováno v:
Moscow J. Comb. Number Th. 11 (2022) 335-372
We study the correlations of pairs of logarithms of positive integers at various scalings, either with trivial weigths or with weights given by the Euler function, proving the existence of pair correlation functions. We prove that at the linear scali
Externí odkaz:
http://arxiv.org/abs/2105.02860
In this survey based on the book by the authors [BPP], we recall the Patterson-Sullivan construction of equilibrium states for the geodesic flow on negatively curved orbifolds or tree quotients, and discuss their mixing properties, emphazising the ra
Externí odkaz:
http://arxiv.org/abs/2010.08212