The Green-Tao theorem for primes of the form x²+y²+1

2017/08/29 by Yu-Chen Sun, Hao Pan, Sun, Yu-Chen +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1708.08629

arxiv created 2017/08/31 · arxiv updated 2017/09/01

Abstract

We prove that the primes of the form x²+y²+1 contain arbitrarily long non-trivial arithmetic progressions.

Related

• Arithmetic progressions of primes in short intervals
• Patterns of primes
• Progressions arithmétiques dans les nombres premiers, d'après B. Green et T. Tao
• Long arithmetic progressions of primes
• Narrow arithmetic progressions in the primes