Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Kurlberg, Par"'
We study the fine distribution of lattice points lying on expanding circles in the hyperbolic plane $\mathbb{H}$. The angles of lattice points arising from the orbit of the modular group $PSL_{2}(\mathbb{Z})$, and lying on hyperbolic circles, are sho
Externí odkaz:
http://arxiv.org/abs/2009.10546
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic eigenfunctions averag
Externí odkaz:
http://arxiv.org/abs/2006.11644
Autor:
Kurlberg, Par, Wigman, Igor
This is a manuscript containing the full proofs of results announced in [KW], together with some recent updates. We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal c
Externí odkaz:
http://arxiv.org/abs/1707.00766
Autor:
Kurlberg, Par, Wigman, Igor
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak limits, ar
Externí odkaz:
http://arxiv.org/abs/1501.01995
Let $\varphi: {\mathbb P}^1 \longrightarrow {\mathbb P}^1$ be a rational map of degree greater than one defined over a number field $k$. For each prime ${\mathfrak p}$ of good reduction for $\varphi$, we let $\varphi_{\mathfrak p}$ denote the reducti
Externí odkaz:
http://arxiv.org/abs/1410.3378
Autor:
Ueberschaer, Henrik, Kurlberg, Par
We consider the Laplacian with a delta potential (a "point scatterer") on an irrational torus, where the square of the side ratio is diophantine. The eigenfunctions fall into two classes ---"old" eigenfunctions (75%) of the Laplacian which vanish at
Externí odkaz:
http://arxiv.org/abs/1409.6878
Autor:
Kurlberg, Par, Wigman, Igor
Publikováno v:
C. R. Math. Acad. Sci. Paris, 353(2):101--104, 2015
We prove that the Nazarov-Sodin constant, which up to a natural scaling gives the leading order growth for the expected number of nodal components of a random Gaussian field, genuinely depends on the field. We then infer the same for "arithmetic rand
Externí odkaz:
http://arxiv.org/abs/1406.7449
Autor:
Ueberschaer, Henrik, Kurlberg, Par
We prove an analogue of Shnirelman, Zelditch and Colin de Verdiere's Quantum Ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There ar
Externí odkaz:
http://arxiv.org/abs/1311.1396
Autor:
Amerik, Ekaterina, Kurlberg, Par, Nguyen, Khoa, Towsley, Adam, Viray, Bianca, Voloch, Jose Felipe
Let f:X->X be a morphism of a variety over a number field K. We consider local conditions and a "Bruaer-Manin" condition, defined by Hsia and Silverman, for the orbit of a point P in X(K) to be disjoint from a subvariety V of X, i.e., the intersectio
Externí odkaz:
http://arxiv.org/abs/1305.4398
Publikováno v:
INTEGERS, 12B (2012/2013): Paper #A4, 9pp
We consider sets of positive integers containing no sum of two elements in the set and also no product of two elements. We show that the upper density of such a set is strictly smaller than 1/2 and that this is best possible. Further, we also find th
Externí odkaz:
http://arxiv.org/abs/1201.1317