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Irreducible algebraic integers in short intervals

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Abstract

We study distribution of irreducible algebraic integers in short intervals and prove that if the class number of an algebraic number field K exceeds 2, every interval of the form (x, x + x θ) with a fixed θ > 1/2 contains absolute value of the norm of an irreducible algebraic integer from K provided x ≥ x 0. The constant x 0 effectively depends on K and θ.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614, Poznan, Poland

    Jerzy Kaczorowski

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  1. Jerzy Kaczorowski
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Correspondence to Jerzy Kaczorowski.

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The author was supported in part by the grant no. N N201 1482 33 from the Polish Ministry of Science and Higher Education.

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Kaczorowski, J. Irreducible algebraic integers in short intervals. Math. Ann. 345, 297–305 (2009). https://doi.org/10.1007/s00208-009-0354-4

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  • DOI: https://doi.org/10.1007/s00208-009-0354-4

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