Polynomial Configurations in the Primes

Authors

Thái Hoàng Lê, Ecole Polytechnique

Document Type

Lecture

Publication Date

11-10-2014

Abstract

The Green–Tao theorem says that the primes contain arithmetic progressions of arbitrary length. Tao and Ziegler extended it to polynomial progressions, showing that configurations {a + P₁(d), …, a + Pₖ(d)} exist in the primes, where P₁, …, Pₖ are polynomials in ℤ[x] without constant terms (thus the Green–Tao theorem corresponds to the case where all the Pᵢ are linear). We extend this result further, showing that we can add the extra requirement that d be of the form p – 1 (or p + 1) where p is prime. This is joint work with Julia Wolf.

Relational Format

presentation

Recommended Citation

Lê, Thái Hoàng, "Polynomial Configurations in the Primes" (2014). Colloquium. 17.
https://egrove.olemiss.edu/math_colloquium/17