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![[parent]](http://images.planetmath.org:8080/images/uparrow.png)
values of the Dedekind zeta function of  at negative integers
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(Example)
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As an example of the parent entry, we exhibit a few values of the Dedekind zeta function $\zeta(s,K)$ associated to the number field $K=\Rats(\sqrt{5})$ The following are the first few values of $\zeta(1-k,K)$ for $k\geq 2$ even ($\zeta(1-k,K)=0$ for odd $k$ :
| $k$ |
$\zeta(1-k,K)$ |
| $2$ |
$1/30$ |
| $4$ |
$1/60$ |
| $6$ |
$67/630$ |
| $8$ |
$361/120$ |
| $10$ |
$412751/1650$ |
| $12$ |
$795286411/16380$ |
| $14$ |
$568591843/30$ |
| $16$ |
$54701427071177/4080$ $18$ |
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"values of the Dedekind zeta function of  at negative integers" is owned by alozano.
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Cross-references: odd, even, number field, Dedekind zeta function
This is version 2 of values of the Dedekind zeta function of  at negative integers, born on 2006-06-20, modified 2006-06-20.
Object id is 8065, canonical name is ValuesOfTheDedekindZetaFunctionOfMathbbQsqrt5AtNegativeIntegers.
Accessed 1317 times total.
Classification:
| AMS MSC: | 11M06 (Number theory :: Zeta and $L$-functions: analytic theory :: $\zeta $) | | | 11R42 (Number theory :: Algebraic number theory: global fields :: Zeta functions and $L$-functions of number fields) |
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Pending Errata and Addenda
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