Modified heat equations for an analytic continuation of the spectral ζ function

2019/03/15 by Zingg, Tobias
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1903.06688

Abstract

For an elliptic differential operator D of order h in n dimensions, the spectral ζ-function ζ_D(s) for \Re s > (n)/(h) can be evaluated as an integral over the heat kernel e^{-t D}. Here, alternative expressions for ζ_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=(m)/(h), m

Related

• Heat Expansion and Zeta
• Green function diagonal for a class of heat equations
• ζ-function and heat kernel formulae
• Heat kernel for higher-order differential operators in Euclidean space
• Evolution equations involving nonlinear truncated Laplacian operators