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

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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.
21 pages, preliminary version. Comments welcome

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Number Theory, Classical Analysis and ODEs, 11N64

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http://salesiana.dossiersoluciones.com/handle/123456789/115285

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608109
 http://arxiv.org/abs/math/0608109

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arXiv