N. Lyall

activity

20062023

most citedDistance Graphs and sets of positive upper density in

R^{d}

13 citations · 43 across the 19 of their papers we have counts for

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Showing 2010 · math.CAShow all

3 papers · 2 filters

math.CA2010★ 6 cited

Optimal Polynomial Recurrence

Neil Lyall, Akos Magyar

Let $P \in Z [n]$ with $P (0) = 0$ and $\VE>0$. We show, using Fourier analytic techniques, that if $N\geq \exp\exp(C\VE^{-1}\log\VE^{-1})$ and $A \subseteq {1, . ˙ ., N}$ , then there must…

math.CA2010★ 1 cited

An optimal version of Sarkozy's theorem

Neil Lyall, Akos Magyar

Using Fourier analytic techniques, we prove that if $\VE>0$, $N\geq \exp\exp(C\VE^{-1}\log\VE^{-1})$ and $A \subseteq {1, ..., N}$ , then there must exist $t \in N$ such that \[\frac{|…

math.CA2010★ 11 cited

Simultaneous Polynomial Recurrence

Neil Lyall, Akos Magyar

Let $A \subseteq {1, ..., N}$ and $P_{1}, ..., P_{ℓ} \in Z [n]$ with $P_{i} (0) = 0$ and $° P_{i} = k$ for every $1 \leq i \leq ℓ$ . We show, using Fourier analytic techniques, that for every $\VE>0…