PlanetMath: generalized Riemann hypothesis

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generalized Riemann hypothesis

(Definition)

This generalization of the Riemann hypothesis to arbitrary Dedekind zeta functions states that for any number field , the only zeroes of the Dedekind zeta function $\zeta_K(s)$ that lie in the strip $0\leq\Re s\leq 1$ satisfy $\Re s=\frac{1}{2}$ .

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Cross-references: number field, Dedekind zeta functions, Riemann hypothesis
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This is version 2 of generalized Riemann hypothesis, born on 2003-08-28, modified 2003-08-29.
Object id is 4662, canonical name is GeneralizedRiemannHypothesis.
Accessed 2355 times total.

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AMS MSC:

11M06 (Number theory :: Zeta and $L$-functions: analytic theory :: $\zeta $)

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