Asymptotic expansion of spectral zeta functions on compact Riemannian manifolds with boundary

What the research examines

This work establishes full asymptotic expansions for the spectral zeta function associated with Laplace-Beltrami operators with mixed Dirichlet-Neumann boundary conditions, resolving a long-standing conjecture regarding logarithmic terms on non-smooth corners.

Why it may matter

Advances fundamental analytical tools in global differential geometry and quantum field theory path integrals.

What to examine carefully

Results require piecewise smooth C^infinity boundary manifolds and do not currently generalize to fractal boundaries.

Try a small, reproducible follow-up

Compute the first three Seeley-Gilkey heat kernel coefficients for the 2D Laplacian on a square billiard domain with mixed boundary conditions.

Questions to investigate

1. How are corner singular contributions separated from smooth boundary geodesic integrals?
2. What are the implications of the analytical continuation poles for Casimir energy regularizations?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources