An improved example for an autoconvolution inequality

2025/06/20 by Boyer, Christopher, Li, Zane Kun · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2506.16750

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a nonnegative step function with 575 equally spaced intervals such that \frac‖f ∗ f‖_L²(ℝ)²‖f ∗ f‖_L^∞(ℝ)‖f ∗ f‖_L¹(ℝ) ≥ 0.901564. This improves upon a recent result of Deepmind's AlphaEvolve, which found a nonnegative step function with 50 equally space intervals for which the left hand side is ≥ 0.8962. Our function was found using simulated annealing and gradient based methods rather than using large language models.

Citations

• On Suprema of Autoconvolutions with an Application to Sidon sets
• Improved bounds on the supremum of autoconvolutions

Cited by

• Further Improvements to the Lower Bound for an Autoconvolution Inequality

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