Improved bounds on the supremum of autoconvolutions

2009/07/08 by Mate Matolcsi, Matolcsi, Mate, Carlos Vinuesa +1 · 7 citations
Mathematics · #11P70 #42A05 #42A85 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:11P70 #msc:42A05 #msc:42A85

paper · pdf · doi:10.48550/arxiv.0907.1379

15 pages. Some typos have been corrected, the best examples have been slightly improved, two plots of them have been included and some remarks have been added

arxiv created 2009/09/04 · arxiv updated 2009/12/01

Abstract

We give a slight improvement of the best known lower bound for the supremum of autoconvolutions of nonnegative functions supported in a compact interval. Also, by means of explicit examples we disprove a long standing natural conjecture of Schinzel and Schmidt concerning the extremal function for such autoconvolutions.

Cited by

• On suprema of convolutions on discrete cubes
• ThetaEvolve: Test-time Learning on Open Problems
• CodeEvolve: An open source evolutionary coding agent for algorithm discovery and optimization
• Further Improvements to the Lower Bound for an Autoconvolution Inequality
• A Randomized Rounding Approach for DAG Edge Deletion
• An improved example for an autoconvolution inequality
• AlphaEvolve: A coding agent for scientific and algorithmic discovery

Related

• The supremum of autoconvolutions, with applications to additive number theory
• Further Improvements to the Lower Bound for an Autoconvolution Inequality
• On classical inequalities for autocorrelations and autoconvolutions
• On Suprema of Autoconvolutions with an Application to Sidon sets
• The first 128 digits of an autoconvolution inequality