Singular Vectors and $ψ$-Dirichlet Numbers over Function Field

We show that the only $ψ$-Dirichlet numbers in a function field over a finite field are rational functions, unlike $ψ$-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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