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
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
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