Adelic Rogers' formula and an application

2024/01/24 by Alam, Mahbub, Strömbergsson, Andreas
#11Hxx #11Jxx #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.13476

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.

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