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arXiv · 2203.09716

Singular Vectors and $\psi$-Dirichlet Numbers over Function Field

Shreyasi Datta·Yewei Xu
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Abstract

We show that the only $\psi$-Dirichlet numbers in a function field over a finite field are rational functions, unlike $\psi$-Dirichlet numbers in $\mathbb{R}$. We also prove that there are uncountably many totally irrational singular vectors with large uniform exponent in quadratic surfaces over a positive characteristic field.

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Shreyasi Datta, Yewei Xu. 2022-03-18. Singular Vectors and $\psi$-Dirichlet Numbers over Function Field. https://arxiv.org/abs/2203.09716

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