E. White

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20182022

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math.CO2022

An almost-tight $L^{2}$ autoconvolution inequality

Ethan Patrick White

Let $F$ denote the set of functions $f : [- 1/2, 1/2] \to R$ such that $\int f = 1$ . We determine the value of $in f_{f \in F} ∥ f * f ∥_{2}$ up…

math.CO2022

Erdős' minimum overlap problem

Ethan Patrick White

We obtain a substantially improved lower bound for the minimum overlap problem asked by Erdős. Our approach uses elementary Fourier analysis to translate the problem to a convex op…

An almost-tight L2 autoconvolution inequality

Erdős' minimum overlap problem

An almost-tight $L^{2}$ autoconvolution inequality