$ζ-$function and heat kernel formulae

We present a systematic study of asymptotic behavior of (generalised) $ζ-$functions and heat kernels used in noncommutative geometry and clarify their connections with Dixmier traces. We strengthen and complete a number of results from the recent literature and answer (in the affirmative) the question raised by M. Benameur and T. Fack \cite{BF}.

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