ζ -function and heat kernel formulae

We present a systematic study of asymptotic behaviour 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 (2006) [1]. © 2010 Elsevier Inc. All rights reserved.