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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2014
    • (edited Aug 25th 2014)

    started some minimum at Bost-Connes system.

    Hm, it seems that the statement is that that partition function of the BC-system

    βTr(exp(βH BostConnes)) \beta \mapsto Tr(\exp(- \beta H_{BostConnes}))

    is the Riemann zeta function. But by the pertinent analogies the zeta functions are not supposed to equal partition functions, but to be related to them by the transformation

    s 0 β s1(Tr(exp(βH))1)dβ. s \mapsto \int_0^\infty \beta^{s-1} \left(Tr(\exp(- \beta H)) -1\right)\; d \beta \,.


    • CommentRowNumber2.
    • CommentAuthorTom Mainiero
    • CommentTimeSep 11th 2023

    Fixed broken link to the Bost-Connes paper.

    diff, v4, current