We show that the only -Dirichlet numbers in a function field over a finite field are rational functions, unlike -Dirichlet numbers in . 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 -Dirichlet dans , les seuls nombres -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.
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Keywords: Singular vectors, Approximation in function field
Datta, Shreyasi 1 ; Xu, Yewei 2
CC-BY-ND 4.0
@article{JTNB_2024__36_3_1021_0,
author = {Datta, Shreyasi and Xu, Yewei},
title = {Singular {Vectors} and $\psi ${-Dirichlet} {Numbers} over {Function} {Field}},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {1021--1038},
year = {2024},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {36},
number = {3},
doi = {10.5802/jtnb.1305},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.1305/}
}
TY - JOUR AU - Datta, Shreyasi AU - Xu, Yewei TI - Singular Vectors and $\psi $-Dirichlet Numbers over Function Field JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 1021 EP - 1038 VL - 36 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://www.numdam.org/articles/10.5802/jtnb.1305/ DO - 10.5802/jtnb.1305 LA - en ID - JTNB_2024__36_3_1021_0 ER -
%0 Journal Article %A Datta, Shreyasi %A Xu, Yewei %T Singular Vectors and $\psi $-Dirichlet Numbers over Function Field %J Journal de théorie des nombres de Bordeaux %D 2024 %P 1021-1038 %V 36 %N 3 %I Société Arithmétique de Bordeaux %U https://www.numdam.org/articles/10.5802/jtnb.1305/ %R 10.5802/jtnb.1305 %G en %F JTNB_2024__36_3_1021_0
Datta, Shreyasi; Xu, Yewei. 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
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