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The short square-set energy conjecture

From papers

Let EE be a set of squares contained in the interval of square roots

E⊂{k2:N≤k≤N+N1−ε}.E\subset\{k^2:N\le k\le N+N^{1-\varepsilon}\}.

The short square-set energy conjecture. One should have

∑mrE+E2(m)≪∣E∣2.\sum_m r_{E+E}^2(m)\ll |E|^2.

The statement appears among the source's open conjectures for square frequencies; the supplied excerpt does not provide a resolution.

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Sources & referencesView supporting material

Primary source

Javier Cilleruelo and Andrew Granville, “Lattice points on circles, squares in arithmetic progressions and sumsets of squares”, arXiv:math/0608109 (2006).

additive-combinatoricsharmonic-analysissquares

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