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

TL;DR
This paper extends the Maynard-Tao theorem to admissible tuples of linear forms with arbitrary leading coefficients in number fields and function fields, broadening the scope of prime tuple results.
Contribution
It generalizes the Maynard-Tao theorem to include linear forms with arbitrary leading coefficients over number and function fields, beyond monic forms.
Findings
Established Maynard-Tao theorem for arbitrary leading coefficients in number fields.
Extended prime tuple results to function fields.
Provided applications of the generalized theorem.
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.
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Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics
