Mertens products in arithmetic progressions over function fields
Number Theory
2026-02-06 v1 Algebraic Geometry
Abstract
We establish a function field analogue of Mertens' formula for Euler products restricted to primes in arithmetic progressions over the polynomial ring F_q[t]. Our results are in direct correspondence with those of Languasco and Zaccagnini for arithmetic progressions in the integers. Over function fields, Weil's Riemann hypothesis for Dirichlet L-functions holds unconditionally, and consequently the analogue of the GRH-strength asymptotic is obtained without any exceptional zero correction term.
Keywords
Cite
@article{arxiv.2602.05788,
title = {Mertens products in arithmetic progressions over function fields},
author = {Hwanyup Jung},
journal= {arXiv preprint arXiv:2602.05788},
year = {2026}
}