Improving the Stewart–Yu bound for all abc triples
Ruiyi Zhang · Preprint, 2026-11-13 · 8 pages
PDFHTMLDOI 10.5281/zenodo.24202155Source and checks
Abstract
For coprime positive integers a + b = c, write R = rad(abc). We prove that log c < A R^(1/3) exp(−log R/(3000 log log R)), where A is absolute and effectively computable. Equivalently, log c < A R^(1/3 − 1/(3000 log log R)), the exponent tending to 1/3 from below. This improves the Stewart–Yu bound log c ≪ R^(1/3)(log R)^3. The proof combines estimates at maximal prime powers with a growing number of auxiliary primes in a rational logarithmic form.
Cite
Ruiyi Zhang, Improving the Stewart–Yu bound for all abc triples, preprint, Zenodo, 2026. https://doi.org/10.5281/zenodo.24202155