Adelic Rogers' formula and an application
Number Theory
2024-01-25 v1
Abstract
Recently, Seungki Kim proved an extension of Rogers' mean value formula to the adeles of an arbitrary number field. In this paper we give a new proof Kim's formula, and give a criterion ensuring convergence in this formula. We also discuss one application, namely diophantine approximation over imaginary quadratic number fields with congruence conditions, where we prove an analogue of a famous counting result of W. M. Schimdt.
Cite
@article{arxiv.2401.13476,
title = {Adelic Rogers' formula and an application},
author = {Mahbub Alam and Andreas Strömbergsson},
journal= {arXiv preprint arXiv:2401.13476},
year = {2024}
}