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The size function for cyclic cubic fields

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada

E-mail Address: hatran1104@gmail.com

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and

Peng Tian

Department of Mathematics, East China University of Science and Technology, Meilong Road 130, 200237, Shanghai, P. R. China

E-mail Address: tianpeng@ecust.edu.cn

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https://doi.org/10.1142/S1793042118500276Cited by:1 (Source: Crossref)

Abstract

The size function for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the trivial class of Arakelov divisors. This conjecture was proved for many number fields with unit groups of rank one. Our research confirms that the conjecture also holds for cyclic cubic fields, which have unit groups of rank two.

Keywords:

AMSC: 11R16, 11Y40, 11H06

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