Mean Values over Lattices in Number Fields and Effective Diophantine Approximation

Nathan Hughes

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arXiv · 2306.02499

Mean Values over Lattices in Number Fields and Effective Diophantine Approximation

Nathan Hughes

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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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Nathan Hughes. 2023-06-04. Mean Values over Lattices in Number Fields and Effective Diophantine Approximation. https://arxiv.org/abs/2306.02499

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