University of Illinois Urbana-Champaign

Correlations of sequences modulo one and statistics of geometrical objects associated to visible points

Chaubey, Sneha

Content Files
CHAUBEY-DISSERTATION-2017.pdf

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https://hdl.handle.net/2142/98203

Description

Title
Correlations of sequences modulo one and statistics of geometrical objects associated to visible points
Author(s)
Chaubey, Sneha
Issue Date
2017-07-10
Director of Research (if dissertation) or Advisor (if thesis)
Zaharescu, Alexandru
Doctoral Committee Chair(s)
Boca, Florin
Committee Member(s)
  • Hildebrand, A. J.
  • Robles, Nicolas
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2017-09-29T17:45:18Z
Keyword(s)
  • Pair correlation
  • Riemann zeta
  • Visible lattice points
Abstract
This thesis is divided into two major topics. In the first, we study the topic of distribution of sequences modulo one. In particular, we look at the spacing distributions between members of rational valued sequences modulo one. We come up with examples of many such sequences which behave as randomly chosen numbers from the unit interval. These include examples from the class of exponentially as well as sub-exponentially growing sequences. In the second part, we examine distribution questions for certain geometrical objects, for example, Farey-Ford and generalized Farey-Ford polygons and Farey-Ford parabolas associated to visible lattice points. As the names suggest, these objects are constructed based on the relation between visible points/Farey fractions and their geometrical interpretation in the form of Ford circles. We study the distribution of moments of various geometrical parameters associated to these objects by giving asymptotic formulas employing tools from analytic number theory.
Graduation Semester
2017-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/98203
Copyright and License Information
Copyright 2017 Sneha Chaubey

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