Year: 2024
Type: preprint
Abstract: We prove analogues of the theorem of Green and Tao on linear constellations in primes, in which the primes under consideration are restricted by certain arithmetic conditions. Our first main result is conditional upon Hooley's Riemann hypothesis and imposes the extra condition that the primes have prescribed primitive roots. Our second main result is unconditional and imposes the extra condition that the primes have prescribed Artin symbols in given Galois number fields. In the appendix we present an application of the second result in inverse Galois theory.
Source: arXiv (Cornell University)
Institution: Graz University of Technology
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403665784