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A DETERMINANT FORMULA FOR RELATIVE CONGRUENCE ZETA FUNCTIONS FOR CYCLOTOMIC FUNCTION FIELDS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  15 July 2010

DAISUKE SHIOMI
DAISUKE SHIOMI*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan (email: m05019e@math.nagoya-u.ac.jp)
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Abstract

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Rosen gave a determinant formula for relative class numbers for cyclotomic function fields, which may be regarded as an analogue of the classical Maillet determinant. In this paper, we give a determinant formula for relative congruence zeta functions for cyclotomic function fields. Our formula may be regarded as a generalization of the determinant formula for the relative class number.

Keywords

congruence zeta functioncyclotomic function fields

MSC classification

Secondary: 11M38: Zeta and $L$-functions in characteristic $p$
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 133 - 144
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

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