Proceedings of the Japan Academy, Series A, Mathematical Sciences

Determinant formulas for zeta functions for real abelian function fields

Daisuke Shiomi

Full-text: Open access

Abstract

In this paper, we will give determinant formulas of zeta functions for real abelian extensions over a rational functions field with one variable. By a class number formula, our formula can be regard as a generalization of determinant formulas of class numbers.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 87, Number 10 (2011), 183-185.

Dates
First available in Project Euclid: 1 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1322748846

Digital Object Identifier
doi:10.3792/pjaa.87.183

Mathematical Reviews number (MathSciNet)
MR2863410

Zentralblatt MATH identifier
1286.11190

Subjects
Primary: 11S40: Zeta functions and $L$-functions [See also 11M41, 19F27] 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

Keywords
Zeta functions cyclotomic function fields

Citation

Shiomi, Daisuke. Determinant formulas for zeta functions for real abelian function fields. Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), no. 10, 183--185. doi:10.3792/pjaa.87.183. https://projecteuclid.org/euclid.pja/1322748846


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References

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