Communications of the
Korean Mathematical Society CKMS

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Commun. Korean Math. Soc. 2012; 27(3): 455-464

Printed September 1, 2012

https://doi.org/10.4134/CKMS.2012.27.3.455

Copyright © The Korean Mathematical Society.

On the relative zeta function in function fields

Daisuke Shiomi

Nagoya University

Abstract

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In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

Keywords: zeta functions, class numbers, function fields

MSC numbers: 11M38, 11R58

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