Lattice points on circles, squares in arithmetic progressions and sumsets of squares
Number Theory
2007-05-23 v1 Classical Analysis and ODEs
Abstract
Rudin conjectured that there are never more than c N^(1/2) squares in an arithmetic progression of length N. Motivated by this surprisingly difficult problem we formulate more than twenty conjectures in harmonic analysis, analytic number theory, arithmetic geometry, discrete geometry and additive combinatorics (some old and some new) which each, if true, would shed light on Rudin's conjecture.
Cite
@article{arxiv.math/0608109,
title = {Lattice points on circles, squares in arithmetic progressions and sumsets of squares},
author = {Javier Cilleruelo and Andrew Granville},
journal= {arXiv preprint arXiv:math/0608109},
year = {2007}
}
Comments
21 pages, preliminary version. Comments welcome