• Corpus ID: 119270042

# 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}
}
• 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…

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics, Materials Science
• 1976
The effective Lagrangian and vacuum energy-momentum tensor $〈{T}^{\ensuremath{\mu}\ensuremath{\nu}}〉$ due to a scalar field in a de Sitter-space background are calculated using the
This paper describes a technique for regularizing quadratic path integrals on a curved background spacetime. One forms a generalized zeta function from the eigenvalues of the differential operator
• Mathematics
• 1977
Infinite products of ratios of eigenvalues of Sturm-Liouville operators are expressed in a closed form in terms of corresponding solutions of initial-value problems. Introduction. Gaussian path
• Mathematics
• 1992
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent
• Mathematics
• 1995
Pseudo-Differential Operators Introduction Fourier Transform and Sobolev Spaces Pseudo-Differential Operators on Rm Pseudo-Differential Operators on Manifolds Index of Fredholm Operators Elliptic
Introduction and Outlook.- Mathematical Formulas Involving the Different Zeta Functions.- A Treatment of the Non-Polynomial Contributions: Application to Calculate Partition Functions of Strings and
• Physics
• 1960
This translation of the survey article by I. M. Gel'fand and A. M. Yaglom on the theory and applications of integration in functional spaces in problems of quantum physics was prepared because it was
• Mathematics