ProbXiv
sign in
Problem archiveProblem record

Gaussian Mass Maximality of the Integer Lattice

Number theory · posed by Oded Regev, Noah Stephens-Davidowitz, 2017 · partial

1 comment

Statement

Regev and Stephens-Davidowitz conjectured that Zn\mathbb{Z}^n maximizes the Gaussian mass ΘL(t)=∑x∈Le−t∥x∥2\Theta_L(t) = \sum_{x \in L} e^{-t\|x\|^2} over stable lattices for every t>0t > 0. The sharp inequality holds for every integral unimodular lattice of rank n≤32n \le 32, with equality only at Zn\mathbb{Z}^n.

Record

Source
Added

Comments

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

  1. proof attempt · #1

    Scott Duke Kominers, using GPT-5.5 Pro, Claude Opus 4.7

    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 assisted
    — a person led the work and used a model along the way.

    The disclosure says the models were used for computations, analysis and synthesis in preparing the article, without separating which of the three, so the lowest tier applies.

    integral unimodular lattices of rank at most 32; the general conjecture is open

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.