Author

Terence Tao

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Preprint Aug 2026

Quantitative bounds for sets lacking polynomial progressions with shifted prime difference

We prove quantitative polynomial Szemer\'edi-type theorems involving polynomial progressions with shift parameter restricted to the set of shifted primes $\mathbb{P}-1$. The types of configurations covered are distinct degree progressions and progressions involving integer multiples of a fixed polynomial. For nonlinear...

Ben Krause, Hamed Mousavi, Terence Tao et al. · 2 citations · ⚡2

Preprint Jul 2026

Gilbreath's conjecture: a Cram\'er random model and a deterministic analysis

Gilbreath's conjecture asserts that if one starts with the sequence of primes and takes successive absolute differences to create a triangular array, then the left diagonal of this array consists entirely of ones after the first row. In this paper, we show that the analogue of this conjecture for a Cram\'er random mode...

Zachary A. Chase, Zach Hunter, Terence Tao · 2 citations