Singular Vectors and ψ-Dirichlet Numbers over Function Field
Shreyasi Datta1 ; Yewei Xu2
1 Department of Mathematics, Heslington, York YO10 5DD University of York United Kingdom
2 Department of Mathematics, University of Wisconsin-Madison 716 Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706 United States of America
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 1021-1038.

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

Nous montrons que contrairement aux nombres ψ-Dirichlet dans ℝ, les seuls nombres ψ-Dirichlet dans un corps de fonctions sur un corps fini sont les fonctions rationnelles. Nous prouvons également qu’il existe une quantité non dénombrable de vecteurs singuliers totalement irrationnels avec un grand exposant uniforme dans les surfaces quadratiques sur un corps de caractéristique positive.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1305
Classification : 11J13, 11J54, 37A44, 11N56, 14G42
Mots-clés : Singular vectors, Approximation in function field

Shreyasi Datta 1 ; Yewei Xu 2

1 Department of Mathematics, Heslington, York YO10 5DD University of York United Kingdom
2 Department of Mathematics, University of Wisconsin-Madison 716 Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706 United States of America
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Shreyasi Datta; Yewei Xu. Singular Vectors and $\psi $-Dirichlet Numbers over Function Field. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 3, pp. 1021-1038. doi : 10.5802/jtnb.1305. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1305/

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