The first 128 digits of an autoconvolution inequality

2026/02/07 by Andrew Rechnitzer · 1 voice
Mathematics · #math.NT #math.CO

paper · pdf

Abstract

Using rigorous high-precision floating point arithmetic we compute very tight rigorous bounds on the auto-convolution constant ν₂² = inf_f ‖f ∗ f‖₂² = inf_f ∫_-1¹ (f ∗ f)² where the infimum is taken over all unit mass functions f ∈ L¹(-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 ν₂², and so substantially improve previous bounds on this quantity due to White, Green, and Martin & O'Bryant.

Citations

• Learning to Discover at Test Time
• Mathematical exploration and discovery at scale
• An almost-tight L² autoconvolution inequality
• How to hunt wild constants
• Arb: Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic
• On Suprema of Autoconvolutions with an Application to Sidon sets
• Generalized Sidon sets
• Generalized Sidon sets
• The supremum of autoconvolutions, with applications to additive number theory
• The Symmetric Subset Problem in Continuous Ramsey Theory
• A Complete Annotated Bibliography of Work Related to Sidon Sequences

Discussions

• arxiv.org/abs/2602.07292 'The first 128 digits of an autoconvolution inequality' - Andrew Rechnitzer [bsky, 1 points, 1 comments]

Related

• The supremum of autoconvolutions, with applications to additive number theory
• Further Improvements to the Lower Bound for an Autoconvolution Inequality
• An almost-tight L² autoconvolution inequality
• On Suprema of Autoconvolutions with an Application to Sidon sets
• An improved example for an autoconvolution inequality