PlanetMath: Siegel-Klingen Theorem

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Siegel-Klingen Theorem

(Theorem)

Theorem 1 (Siegel-Klingen Theorem, [1],[2]) Let be a totally real number field and let $\zeta(s,K)$ be the Dedekind zeta function of . If $n\geq 1$ is an integer then $\zeta(-n,K)$ is a rational number (i.e. $\zeta(-n,K)\in \mathbb{Q}$ ).

Bibliography

1: Klingen, Helmut, Über die Werte der Dedekindschen Zetafunktion. (German) Math. Ann. 145 1961/1962 265-272.
2: Siegel, Carl Ludwig, Über die analytische Theorie der quadratischen Formen. III. (German) Ann. of Math. (2) 38 (1937), no. 1, 212-291.

"Siegel-Klingen Theorem" is owned by alozano.

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Cross-references: rational number, integer, Dedekind zeta function, field, real number
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This is version 1 of Siegel-Klingen Theorem, born on 2006-06-20.
Object id is 8061, canonical name is SiegelKlingenTheorem.
Accessed 593 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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