Equidistribution and primes

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

We begin by reviewing various classical problems concerning the existence of primes or numbers with few prime factors as well as some of the key developments towards resolving these long standing questions. Then we put the theory in a natural and general geometric context of actions on affine n-space and indicate what can be established there. The methods used to develop a combinational sieve in this context involve automorphic forms, expander graphs and unexpectedly arithmetic combinatorics. Applications to classical problems such as the divisibility of the areas of Pythagorean triangles and of the curvatures of the circles in an integral Apollonian packing, are given.

Original languageEnglish (US)
Title of host publicationDifferential Geometry, Mathematical Physics, Mathematics and Society Part 2
Pages225-240
Number of pages16
Edition322
StatePublished - Dec 1 2008

Publication series

NameAsterisque
Number322
ISSN (Print)0303-1179

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Affine orbits
  • Expanders and sumproduct
  • Primes
  • Saturation numbers
  • Sieves

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    Sarnak, P. C. (2008). Equidistribution and primes. In Differential Geometry, Mathematical Physics, Mathematics and Society Part 2 (322 ed., pp. 225-240). (Asterisque; No. 322).