Lattice points on circles, squares in arithmetic progressions and sumsets of squares

Details Lattice points on circles, squares in arithmetic progressions and sumsets of squares Lattice points on circles, squares in arithmetic progressions and sumsets of squares

2006-08-03

arxiv.org/abs/math/0608109v1

Mathematics

Number Theory

21 pages, preliminary version. Comments welcome

Scientific paper

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.

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