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Values of zeta functions and class number 1 criterion for the simplest cubic fields

Published online by Cambridge University Press:  22 January 2016

Hyun Kwang Kim  and
Hyung Ju Hwang
Hyun Kwang Kim
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, San 31 Hyoja Dong, Pohang, 790-784, Korea, hkkim@postech.ac.kr
Hyung Ju Hwang
Affiliation:
Department of Mathematics, Brown University, Providence, RI 02912, U.S.A., hjhwang@math.brown.edu
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Abstract

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Let K be the simplest cubic field defined by the irreducible polynomial

where m is a nonnegative rational integer such that m2 + 3m + 9 is square-free. We estimate the value of the Dedekind zeta function ζK(s) at s = −1 and get class number 1 criterion for the simplest cubic fields.

Keywords

11R1611R42
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 160 , 2000 , pp. 161 - 180
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

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