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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:analyticContinuation
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entire function except simple pole at s=1
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gptkbp:citation
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gptkb:Encyclopedia_of_Mathematics
gptkb:MathWorld
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gptkbp:defines
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sum over nonzero ideals of the ring of integers of a number field
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gptkbp:domain
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algebraic number field
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gptkbp:Euler_product
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product over prime ideals
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gptkbp:field
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number theory
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gptkbp:functionalEquation
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satisfies functional equation similar to Riemann zeta function
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gptkbp:generalizes
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gptkb:Riemann_zeta_function
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gptkbp:hasPoleAt
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s=1
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gptkbp:hasSpecialCase
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Riemann zeta function when K=Q
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https://www.w3.org/2000/01/rdf-schema#label
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Dedekind zeta function
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gptkbp:meromorphic
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true
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gptkbp:namedAfter
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gptkb:Richard_Dedekind
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gptkbp:notation
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ζ_K(s)
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gptkbp:orderOfPoleAtS=1
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1
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gptkbp:relatedTo
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L-functions
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gptkbp:residueAtS=1
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related to class number, regulator, and discriminant of K
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gptkbp:studiedIn
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algebraic number theory
analytic number theory
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gptkbp:usedIn
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class number formula
distribution of prime ideals
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gptkbp:variant
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complex variable s
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gptkbp:bfsParent
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gptkb:lion
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gptkbp:bfsLayer
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4
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