Mean Values over Lattices in Number Fields and Effective Diophantine Approximation
Number Theory
2023-06-06 v1 Dynamical Systems
Abstract
We answer a question raised by Alam and Ghosh concerning an error term for a spiralling result in Diophantine approximation by rationals in a number field. The proof relies on a generalisation of Rogers' Mean Value Theorem to algebraic number fields and an effective ergodic theorem due to Gaposhkin.
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Cite
@article{arxiv.2306.02499,
title = {Mean Values over Lattices in Number Fields and Effective Diophantine Approximation},
author = {Nathan Hughes},
journal= {arXiv preprint arXiv:2306.02499},
year = {2023}
}
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18 pages