Projects per year
Abstract
A celebrated and deep result of Green and Tao states that the primes
contain arbitrarily long arithmetic progressions. In this note, I
provide a straightforward argument demonstrating that the primes get arbitrarily close
to arbitrarily long arithmetic progressions. The argument also applies
to “large sets” in the sense of the Erdős conjecture on arithmetic
progressions. The proof is short, completely selfcontained, and aims to
give a heuristic explanation of why the primes, and other large sets,
possess arithmetic structure.
Original language  English 

Pages (fromto)  553558 
Number of pages  6 
Journal  The American Mathematical Monthly 
Volume  126 
Issue number  6 
Early online date  29 May 2019 
DOIs  
Publication status  Published  May 2019 
Keywords
 Arithmetic progression
 Primes
 GreenTao Theorem
 ErdősTuran Conjecture
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Dive into the research topics of 'Almost arithmetic progressions in the primes and other large sets'. Together they form a unique fingerprint.Projects
 2 Finished

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
1/02/18 → 11/06/21
Project: Standard

Fractal Geometry and Dimension: Fractal Geometry and dimension theory
1/09/16 → 30/06/18
Project: Fellowship