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

Shreyasi Datta; Yewei Xu

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

Number Theory 2022-08-04 v2 Dynamical Systems

Authors: Shreyasi Datta , Yewei Xu

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.

Keywords

fields

Cite

@article{arxiv.2203.09716,
  title  = {Singular Vectors and $\psi$-Dirichlet Numbers over Function Field},
  author = {Shreyasi Datta and Yewei Xu},
  journal= {arXiv preprint arXiv:2203.09716},
  year   = {2022}
}

Comments

We have split version 1 into two parts. The present paper addresses totally irrational singular vectors and $psi$-Dirichlet numbers in function field

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