# relationship between Connes trace formula and Weil's trace formula

Connes trace formula $$Tr{U(h)}=2h(1)log\Lambda + \sum_{v} \int d^{*}x \frac{h(u^{-1})}{|1-u|}$$

Weil's trace $$\int_{C}h(u)|u|d^{*}u- \sum_{\rho}\int_{C}h(u)|u|^{\rho}d^{*}u+\int_{C}h(u)d^{*}u=\sum_{v} \int d^{*}x \frac{h(u^{-1})}{|1-u|}$$

in both cases the right side is quite similar.. but are these two traces equivalent ??

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 You might want to give more context. For example, in what circumstances are these trace formulae being used? And could you define at least some of the notation being used? – M Turgeon Aug 12 '12 at 16:15