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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 30, Issue 3


The least unramified prime which does not split completely

Asif ZamanORCID iD: http://orcid.org/0000-0001-5782-7373
Published Online: 2017-08-30 | DOI: https://doi.org/10.1515/forum-2017-0081


Let K/F be a finite extension of number fields of degree n2. We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal 𝔭 of F which is degree 1 over and does not ramify or split completely in K. We improve upon the previous best known general estimates due to Li [7] when F=, and Murty and Patankar [9] when K/F is Galois. Our bounds are the first when K/F is not assumed to be Galois and F.

Keywords: Non-split prime; prime ideals

MSC 2010: 11R44; 11R42


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About the article

Received: 2017-04-12

Revised: 2017-08-09

Published Online: 2017-08-30

Published in Print: 2018-05-01

Citation Information: Forum Mathematicum, Volume 30, Issue 3, Pages 651–661, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0081.

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