# Modified heat equations for an analytic continuation of the spectral $\zeta$ function

@article{Zingg2019ModifiedHE, title={Modified heat equations for an analytic continuation of the spectral \$\zeta\$ function}, author={T. Zingg}, journal={arXiv: Mathematical Physics}, year={2019} }

For an elliptic differential operator $D$ of order $h$ in $n$ dimensions, the spectral $\zeta$-function $\zeta_D(s)$ for $\Re s > \frac{n}{h}$ can be evaluated as an integral over the heat kernel $e^{-t D}$. Here, alternative expressions for $\zeta_D(s)$ are presented involving an integral over kernels $k_{n,m}$ for a modified heat equation, such that the integral is non-singular around $s=0$, respectively close to potential poles around $s=\frac{m}{h}, m<n$. Besides explicit expressions for an…

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