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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / 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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Volume 30, Issue 3

Issues

Estimates of lattice points in the discriminant aspect over abelian extension fields

Wataru TakedaORCID iD: http://orcid.org/0000-0002-7059-2190 / Shin-ya Koyama
Published Online: 2017-10-06 | DOI: https://doi.org/10.1515/forum-2017-0152

Abstract

We estimate the number of relatively r-prime lattice points in Km with their components having a norm less than x, where K is a number field. The error terms are estimated in terms of x and the discriminant D of the field K, as both x and D grow. The proof uses the bounds of Dedekind zeta functions. We obtain uniform upper bounds as K runs through number fields of any degree under assuming the Lindelöf hypothesis. We also show unconditional results for abelian extensions with a degree less than or equal to 6.

Keywords: Lattice point; approximation formula; Lindelöf hypothesis in the discriminant aspect

MSC 2010: 11N45; 11P21; 11R42; 52C07

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About the article


Received: 2017-07-16

Revised: 2017-09-15

Published Online: 2017-10-06

Published in Print: 2018-05-01


Citation Information: Forum Mathematicum, Volume 30, Issue 3, Pages 767–773, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0152.

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