Primes in Tuples of Linear Forms in Number Fields and Function Fields

2024/09/07 by Rahaman, Habibur
#11N05 #11N36 #11T06 (Primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.04705

Abstract

Following the work of Castillo-Hall-Oliver-Pollack-Thompson who extended Maynard-Tao theorem on admissible tuples to number fields and function fields for tuples with monic linear forms, here we obtain the Maynard-Tao theorem for admissible tuples of linear forms with arbitrary leading coefficients in number fields and function fields. Also, we provide some applications of our results.

Related

• Bounded gaps between primes in number fields and function fields
• A note on the theorem of Maynard and Tao
• Prime polynomial values of linear functions in short intervals
• Linear patterns of prime elements in number fields
• Exponential sums in prime fields for modular forms