Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz

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  • 7/29/2019 Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz

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    R e ( s ) =

    0

    Z e r o e s

    i n s t r i p m u s

    t l i e o n

    R e ( s ) =

    1 / 2

    R e ( s ) =

    0

    R e ( s ) =

    1

    R e ( s ) =

    0

    R e s ) =

    1

    R e ( s ) =

    1

    GRH DZH KNOWN

    DontCare

    DontCare

    Im(s)=0 Im(s)=0 Im(s)=0

    Zeroes

    NO NO

    Zeroes

    NO

    Zeroes

    NO

    Zeroes

    ?

    Sufficiently

    Effective

    Density

    Estimate

    Dependenceof

    Density

    Kon

    unknown

    (1+[K:Q]+log d )Kc

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