Bounds for sets with no polynomial progressions — mentioned by pure-awesome

Wed, 04 Dec 2019 15:13:08 GMT

The abstract of the paper (https://arxiv.org/abs/1909.00309) says > Let P1, … , Pm ∈ Z[y] be polynomials with distinct degrees ... progressions of the form x, x+P1(y), … , x+Pm(y) Such progressions are a generalization of the "shifted geometric" progressions described in the article. In particular, let P1 to Pm be y^i for i=1,...,m. Consider, say, x=0 and y = 3. Then the above gives us: 0, 3, 9, 27, ... , 3^m Which is (almost) a geometric progression. We can "shift" it by setting e.g. x = 1. Though of course the polynomials can be much more general than just y^i. The article says: > In the…

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Bounds for sets with no polynomial progressions — mentioned by notelonmusk

Mon, 02 Dec 2019 22:09:12 GMT

Bounds for sets with no polynomial progressions Abstract: Let P_1,..., P_m ∈ Z[y] be polynomials with distinct degrees, each having zero constant term. We show that any subset A of {1,..., N} with no nontrivial progressions of the form x, x + P_1(y),..., x + P_m(y) has size |A| ≪ N/(log log N)^(cP1,...,Pm) . Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms. [-1] https://arxiv.org/pdf/1909.00309.pdf

Paper and discussion history. A mention is not an endorsement.

Bounds for sets with no polynomial progressions · HackerPapers discussions

Bounds for sets with no polynomial progressions — mentioned by pure-awesome

Bounds for sets with no polynomial progressions — mentioned by notelonmusk