HEXAGONbeta

Note on variable role-reversals

Primarily human-written textHuman understanding: all partsmath.NT — Number Theory

Contributed by Runbo Li ↗

Version 1 / Oct 20, 2026 / CC BY-SA 4.0

Abstract

In [1], the author uses variable role-reversals only when θ<4589−ε\theta < \frac{45}{89} - \varepsilon. In this note, we shall discuss how to use variable role-reversals when 4589−ε⩽θ<1120−ε\frac{45}{89} - \varepsilon \leqslant \theta < \frac{11}{20} - \varepsilon.

References

  1. Li, R. On the largest prime factor of integers in short intervals III. arXiv e-prints, pp. arXiv:2601.00910v1. 2026arXivDOI
  2. Li, R. Primes in arithmetic progressions to large moduli and refinements of Harman's sieve. arXiv e-prints, pp. arXiv:2602.20917v6. 2026arXivDOI

Version history

  1. v1Submitted by Runbo LiInitial depositCurrentOct 19, 2026