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arXiv · 2602.07292

The first 128 digits of an autoconvolution inequality

Andrew Rechnitzer
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Abstract

Using rigorous high-precision floating point arithmetic we compute very tight rigorous bounds on the auto-convolution constant \[ \nu_2^2 = \inf_f \|f \ast f\|_2^2 = \inf_f \int_{-1}^1 (f \ast f)^2 \] where the infimum is taken over all unit mass functions $f \in L^1(-1/2,1/2)$. This quantity arises in additive combinatorics, particularly in the study of Sidon sets. Our bounds give the first 128 digits of $\nu_2^2$, and so substantially improve previous bounds on this quantity due to White, Green, and Martin & O'Bryant.

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Andrew Rechnitzer. 2026-02-07. The first 128 digits of an autoconvolution inequality. https://arxiv.org/abs/2602.07292

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