Pólya's Conjecture for Neumann Balls in Dimensions Three and Higher
Statement
Pólya conjectured in 1954 that the Weyl-law expression bounds the eigenvalue counting function of the Laplacian. The paper proves the Neumann case for Euclidean balls in dimensions three and higher, extending the authors' earlier planar and Dirichlet results. Key difficulty: estimating zeros of derivatives of ultraspherical Bessel functions rather than of Bessel functions themselves.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Nikolay Filonov, Michael Levitin, Iosif Polterovich and David A. Sher, using ChatGPT + Claude (several models)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.
The paper carries an AI usage disclosure: several models of ChatGPT and Claude were used for mathematical discussions and editorial assistance, and all AI-assisted arguments and computations were independently checked by the authors, who take full responsibility. The disclosure does not separate which arguments were AI-assisted, so the lowest tier applies.
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