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Landau's problems through ratios of LL-functions

A mix of human-written and AI-generated textHuman understanding: all partsmath.NT — Number Theory

Contributed by Haozhe Gou, Victor Wang ↗, Max Wenqiang Xu ↗

Version 1 / Nov 13, 2026 / CC BY 4.0

Abstract

Very recently, Lee announced a proof of the Twin Prime Conjecture assuming the Ratios Conjecture for the Riemann zeta function. We obtain conditional asymptotic formulas with power-saving errors for each of Landau's four prime problems. Similar results may be possible for other problems in analytic number theory.

Author comments: 36 pages

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Version history

  1. v1 · 36 pagesSubmitted by Victor Wang36 pagesCurrentNov 13, 2026