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March 2009 A note on algebraic integers with prescribed factorization properties in short intervals
Jerzy Kaczorowski
Funct. Approx. Comment. Math. 40(1): 151-154 (March 2009). DOI: 10.7169/facm/1238418805

Abstract

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 $\theta$.

Citation

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Jerzy Kaczorowski. "A note on algebraic integers with prescribed factorization properties in short intervals." Funct. Approx. Comment. Math. 40 (1) 151 - 154, March 2009. https://doi.org/10.7169/facm/1238418805

Information

Published: March 2009
First available in Project Euclid: 30 March 2009

zbMATH: 1234.11152
MathSciNet: MR2527636
Digital Object Identifier: 10.7169/facm/1238418805

Subjects:
Primary: 11R27
Secondary: 11N25, 11R42, 11R45

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.40 • No. 1 • March 2009
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