Evaluation of zeta function of the simplest cubic field at negative odd integers
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SCOPUS
- Title
- Evaluation of zeta function of the simplest cubic field at negative odd integers
- Authors
- Kim, HK; Kim, JS
- Date Issued
- 2002-01
- Publisher
- AMER MATHEMATICAL SOC
- Abstract
- In this paper, we are interested in the evaluation of the zeta function of the simplest cubic field. We first introduce Siegel's formula for values of the zeta function of a totally real number field at negative odd integers. Next, we will develop a method of computing the sum of a divisor function for ideals, and will give a full description for a Siegel lattice of the simplest cubic field. Using these results, we will derive explicit expressions, which involve only rational integers, for values of a zeta function of the simplest cubic field. Finally, as an illustration of our method, we will give a table for zeta values for the first one hundred simplest cubic fields.
- Keywords
- the simplest cubic field; zeta function; Siegel lattice; VALUES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/19101
- DOI
- 10.1090/S0025-5718-02-01395-9
- ISSN
- 0025-5718
- Article Type
- Article
- Citation
- MATHEMATICS OF COMPUTATION, vol. 71, no. 239, page. 1243 - 1262, 2002-01
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