Nodal Intersections for Arithmetic Random Waves Against a Surface
نویسندگان
چکیده
منابع مشابه
Unlikely Intersections in Arithmetic Dynamics
Combining ideas of Ihara-Serre-Tate, Lang [5] proved the following natural result. If a (complex, irreducible) plane curve C ⊂ A contains infinitely many points with both coordinates roots of unity, then C is the zero locus of an equation of the form xy = ζ, where a, b ∈ Z and ζ is a root of unity. In other words, if F ∈ C[x, y] is an irreducible polynomial for which there exist infinitely many...
متن کاملSurface/surface Intersections: a Three States Classification
Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. In this paper, we introduce a new strategy to classify surfaces against their intersection status. We replace exact geometric entities by fuzzy geometric ones. Intersecting surfaces are then replaced by fuzzy intersecting faces and their fuzzy intersection algori...
متن کاملIntersections of Random Lines
We have three overlapping planar sets within a bounded window. These sets do not have to be convex, or even connected domains. We find a simple expression for the probability that random straight lines across two of the sets intersect within the third. The lines are taken uniformly at random from beams of parallel lines, with the orientations of the beams from an arbitrary joint distribution. T...
متن کاملGeodesic Intersections in Arithmetic Hyperbolic 3-manifolds
It was shown by Chinburg and Reid that there exist closed hyperbolic 3-manifolds in which all closed geodesics are simple. Subsequently, Basmajian and Wolpert showed that almost all quasi-Fuchsian 3-manifolds have all closed geodesics simple and disjoint. The natural conjecture arose that the Chinburg-Reid examples also had disjoint geodesics. Here we show that this conjecture is both almost tr...
متن کاملConvex hull for intersections of random lines
Numerous problems can be reduced to finding the convex hull of a set of points – halfspace intersection, Delaunay triangulation, etc. An algorithm for finding the convex hull in the plane, known as Graham scan [5], achieves an O(n log n) running time. This algorithm is optimal in the worst case. Another algorithm [6] for the same problem runs in O(nh) time, where h is the number of hull points,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Henri Poincaré
سال: 2019
ISSN: 1424-0637,1424-0661
DOI: 10.1007/s00023-019-00831-1