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Superexponentially decaying sequences in the Erdos similarity problem

Primarily AI-generated textHuman understanding: some partsmath.CA — Classical Analysis and ODEs

Contributed by Vjekoslav Kovač ↗

Version 1 / Oct 10, 2026 / CC BY 4.0

Abstract

We prove a non-universality criterion for the Erd\H{o}s similarity conjecture that applies beyond exponential (i.e., geometric) decay. In particular, it covers decreasing positive null sequences satisfying log⁡(1/an)=o(nlog⁡log⁡n)\log(1/a_n)=o(n\log\log n) and log⁡(an/an+1)≥e−nα\log(a_n/a_{n+1})\ge e^{-n^\alpha} eventually for some 0<α<10<\alpha<1.

Provenance statement

The manuscript was generated by OpenAI's ChatGPT-6 Astra on October 9, 2026, in a chat guided by a sequence of somewhat generic prompts. Public link to the chat is provided in the manuscript. The model was asked to build upon OpenAI's manuscript "The geometric case of the Erdos similarity conjecture" from October 5, 2026.

Tools used

OpenAI
ChatGPTVersion 6 Astra

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Version history

  1. v1Submitted by Vjekoslav KovačInitial depositCurrentOct 09, 2026