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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

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


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Band 30, Heft 3

Hefte

The least unramified prime which does not split completely

Asif ZamanORCID iD: http://orcid.org/0000-0001-5782-7373
Online erschienen: 30.08.2017 | DOI: https://doi.org/10.1515/forum-2017-0081

Abstract

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

References

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Artikelinformationen


Erhalten: 12.04.2017

Revidiert: 09.08.2017

Online erschienen: 30.08.2017

Erschienen im Druck: 01.05.2018


Quellenangabe: Forum Mathematicum, Band 30, Heft 3, Seiten 651–661, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0081.

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