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Hilbert-type inequality with primes

Primarily human-written textHuman understanding: all partsmath.NT — Number Theorymath.CA — Classical Analysis and ODEs

Contributed by Kannan Soundararajan ↗

SubmitterKannan Soundararajan

Version 1 / Sep 28, 2026 / CC BY 4.0

Abstract

This note answers a problem posed in Montgomery's CBMS book. The proof was found by ChatGPT 6, and written up by the author.

Provenance statement

As mentioned in the abstract and the paper, the proof was obtained by ChatGPT and written up by the author.

References

  1. H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis , CBMS Regional Conference Series in Mathematics, vol. 84, American Mathematical Society, Providence, RI, 1994.
  2. H. L. Montgomery and R. C. Vaughan, Multiplicative Number Theory I. Classical Theory , Cambridge Studies in Advanced Mathematics, vol. 97, Cambridge University Press, 2007.
  3. Brad Rodgers, On the optimal constant in the Montgomery-Vaughan weighted Hilbert inequality , preprint, arXiv:2608.12315v1 , (2026).arXiv
  4. E. M. Stein, Harmonic Analysis: Real-variable methods, Orthogonality, and Oscillatory Integrals . Princeton Mathematical Series, vol. 43, Princeton University Press, 1993.

Version history

  1. v1Initial depositCurrentSep 28, 2026