ProbXiv
sign in
Problem archiveProblem record

Lower Bounds for Lebesgue Constants and an Erdős-Turán Interpolation Problem

Analysis · posed by Paul Erdős, Pál Turán (interpolation problem), 1937 · solved

1 comment

Statement

Localizing Bernstein theory to prove lower bounds for the Lebesgue constants of Lagrange interpolation, with application to a problem of Erdős and Turán and to a conjectured bound from the interpolation literature.

Record

Source
Added

Comments

No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Terence Tao, using AlphaEvolve, ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    "After some experimentation using the tool AlphaEvolve, the author was led to conjecture a proof of (1.29) by separately lower bounding each of these two factors. The first of these conjectures was then proven by ChatGPT, and the author was able to prove the second, thus giving a complete proof." Figures generated by Gemini.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.