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

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
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