Ruiyi Zhang

Independent researcher in mathematics

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The abc conjecture

Improving the Stewart–Yu bound for all abc triples
Preprint, 2026-11-13 · 8 pages
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Cubic sieves, a primitive-ratio cut and a 20/37 bound for the abc exceptional set
Preprint, 2026-10-09 · 41 pages
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A primitive-ratio cut and a 7/12 bound for the abc exceptional set
Preprint, 2026-10-08 · 16 pages
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An Aggregate CM-Pair Estimate and a 5/3 Bound for Valuation Products of abc Triples
Preprint, 2026-10-08 · 18 pages
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Goldbach-type problems and primes in progressions

Theorem (1 + 1.75) on the Goldbach conjecture
Preprint, 2026-11-12 · 106 pages
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Theorem (1 + 1.8) on the Goldbach conjecture
Preprint, 2026-10-25 · 102 pages
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Shifted primes in arithmetic progressions to large moduli with linear sieve remainder weights
Preprint, 2026-10-24 · 75 pages
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The Goldbach exceptional set: an exponent 11/20
Preprint, 2026-10-15 · 35 pages
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Lacunary series

The irrationality exponent of small-height lacunary series✓ Lean 4 verified · 3 standard axioms only
Preprint, 2026-11-08 · 12 pages
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The irrationality exponent of small-height binary lacunary series is 2
Preprint, 2026-11-07 · 12 pages
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Radicals of consecutive integers

A power saving below two-thirds for equal radicals of consecutive products
Preprint, 2026-11-06 · 61 pages
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Equal radicals of consecutive products
Preprint, 2026-10-29 · 12 pages
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Irrationality of polylogarithms

Irrationality of the trilogarithm at reciprocals of integers of absolute value at least 27
Preprint, 2026-10-15 · 33 pages
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Irrationality of the trilogarithm at reciprocals of large integers
Preprint, 2026-10-13 · 29 pages
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Irrationality of the dilogarithm at reciprocals of integers✓ Lean 4 verified · 3 standard axioms only
Preprint, 2026-10-11 · 57 pages
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Irrationality of the dilogarithm at 1/2✓ Lean 4 verified · 3 standard axioms only
Preprint, 2026-10-09 · 20 pages
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Irrationality of the dilogarithm at 1/3
Preprint, 2026-10-08 · 24 pages
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Irrationality of the dilogarithm at −1/2
Preprint, 2026-10-08 · 23 pages
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Irrationality of the dilogarithm at 1/4
Preprint, 2026-09-13 · 12 pages
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