2 problems

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Brownell's three-term heat trace conjecture for polygons
Let $\Omega$ be a planar polygonal domain, and let $Z(t)$ denote its heat trace for the relevant boundary condition. Brownell's conjecture. The heat trace of a polygon has only thr…
Conjectureopenheat-traces polygonal-domains spectral-geometryarXiv posted 2 days ago
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Berkeley-Keenan conjecture on the next term of the LQG eigenvalue asymptotics
Let $\textbackslash Sigma$ be an LQG domain, let $\textbackslash N(\textbackslash lambda)$ denote its eigenvalue counting function, and consider the next-order term beyond the lead…
Conjectureopeneigenvalue-asymptotics heat-traces liouville-quantum-gravityarXiv posted 2 days ago

Brownell's three-term heat trace conjecture for polygons