We study the distribution of algebraic integers with prescribed factorization
properties in short intervals and prove that for a large class of such numbers
from a fixed algebraic number field $K$ with a non-trivial class group, every
interval of the form $(x, x+x^{\theta})$ with a fixed $\theta >1/2$ contains
absolute value of the norm of such algebraic integer provided $x\geq x_0$. The
constant $x_0$ effectively depends on $K$ and $\theta$.
Publié le : 2009-03-15
Classification:
Factorization in algebraic number fields,
short intervals,
unique factorization,
11R27,
11R42,
11R45,
11N25
@article{1238418805,
author = {Kaczorowski, Jerzy},
title = {A note on algebraic integers with prescribed factorization properties in short intervals},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 151-154},
language = {en},
url = {http://dml.mathdoc.fr/item/1238418805}
}
Kaczorowski, Jerzy. A note on algebraic integers with prescribed factorization properties in short intervals. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 151-154. http://gdmltest.u-ga.fr/item/1238418805/