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# Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form $x^{\gamma}\phi(\log x)$ for a suitable exponent $\gamma$ and $\phi$ a periodic function. We also discuss similar results for the heat content of affine nested fractals.