Home
Resource
The number of lattice points in irrational polytopes
PDF
PDF format is widely accepted and good for printing.
Plug-in required
PDF-1(610.17 kb)
Citation & Export
View Usage Statistics
Staff View

Citation & Export
Hide

Simple citation

Borda, Bence. The number of lattice points in irrational polytopes. Retrieved from https://doi.org/doi:10.7282/T36D5W4J

Export

Click here for information about Citation Management Tools at Rutgers.

Statistics
Hide

Description

TitleThe number of lattice points in irrational polytopes
NameBorda, Bence (author); Beck, Jozsef (chair); Iwaniec, Henryk (internal member); Kopparty, Swastik (internal member); Bumby, Richard (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2016
Other Date2016-05 (degree)
SubjectMathematics, Lattice theory, Polytopes
Extent1 online resource (v, 113 p. : ill.)
DescriptionThe discrepancy | t P ∩ Z^d | - lambda (P) t^d is studied as a function of the real variable t>1, where P is a polytope in R^d with at least one vertex not in Z^d. For a special class of cross polytopes and orthogonal simplices defined in terms of algebraic numbers the discrepancy is proved to be the sum of an explicit polynomial of t and a randomly fluctuating term of smaller order of magnitude. This phenomenon has not yet been described in the literature for any convex body. A general discrepancy bound is proved for polytopes the coordinates of the vertices of which all belong to a given real quadratic field. As a corollary a new property of the regular dodecahedron is obtained. Finally, answering a question of Beck, a formula is given for the variance of a random fluctuation arising in a lattice point counting problem on the plane. The main methods used are Fourier analysis and the theory of Diophantine approximation.
NotePh.D.
NoteIncludes bibliographical references
Noteby Bence Borda
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T36D5W4J
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
Version 8.5.5
Rutgers University Libraries - Copyright ©2024