The Goldbach exceptional set: an exponent 11/20
Ruiyi Zhang · Preprint, 2026-10-15 · 35 pages
PDFHTMLDOI 10.5281/zenodo.23396431Source and checks
Abstract
We prove E(X) ≪_ε X^(11/20+ε) for every ε > 0. Here E(X) counts the positive even integers at most X that are not sums of two primes. A four-level Harman decomposition gives a signed prime minorant. Exact rational bounds for four discarded families give a positive lower bound for its logarithmically weighted mass. We prove a Bombieri–Vinogradov estimate at level X^(9/20−η), with both maxima and a divisor weight. We also bound the exponential sum of the same weight on the minor arcs. The major arcs use classical zero-density estimates and the zero-free half-plane Re s > 7/8 of OpenAI (The Quasi-Riemann Hypothesis, Theorem 1.1).
Cite
Ruiyi Zhang, The Goldbach exceptional set: an exponent 11/20, preprint, Zenodo, 2026. https://doi.org/10.5281/zenodo.23396431