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An autocorrelation problem related to difference bases (AlphaEvolve problem 6)

An autocorrelation problem related to difference bases (AlphaEvolve problem 6). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

MSC 42A85 · Convolution, factorization for one variable harmonic analysisMSC 11B13 · Additive bases, including sumsets

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Licensed source statementAs of Repository at commit 8f44745 (2026-07-11); the repository records AlphaEvolve results, not current research statusSource & evidence ↓
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Problem statement

Let CC be the smallest constant such that

min⁡0≤t≤1∫Rf(x)f(x+t)dx≤C∥f∥L1(R)2\min_{0 \leq t \leq 1} \int_\mathbb{R} f(x) f(x+t) dx \leq C \|f\|_{L^1(\mathbb{R})}^2

for f∈L1(R)f \in L^1(\mathbb{R}). What is CC?

Lean 4

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Background

Repository result category: worse than record — AlphaEvolve did not reach the best known result. See Section 6.2 in "Mathematical Exploration and Discovery at Scale " paper: arXiv:2511.02864. Experiment notebook.

Progress & source assessment

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References
  1. [1]Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Repository of problems accompanying “Mathematical exploration and discovery at scale” (arXiv:2511.02864), github.com/google-deepmind/alphaevolve_repository_of_problems (commit 8f44745, 11 July 2026). — An autocorrelation problem related to difference bases (AlphaEvolve problem 6) linkApache-2.0 (repository license); problem pages reproduced with attribution.

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