• Corpus ID: 119270042

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

  title={Modified heat equations for an analytic continuation of the spectral \$\zeta\$ function},
  author={T. Zingg},
  journal={arXiv: Mathematical Physics},
  • T. Zingg
  • Published 15 March 2019
  • Mathematics
  • arXiv: Mathematical Physics
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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