Abstract: The classical Weyl law gives an asymptotic formula for the counting function of the eigenvalues of the Laplacian on a compact Riemannian manifold. Selberg introduced the trace formula in part to extend the Weyl law to congruence subgroups of \(SL_2(R)\). However, the work of Phillips and Sarnak indicates that this fails dramatically in the non-arithmetic case. Lindenstrauss and Venkatesh proved the Weyl law for the cuspidal spectrum of general congruence locally symmetric spaces. Using recent work of Finis and Matz we give a power saving estimate on the error term of the Weyl law for the cuspidal spectrum. Joint work with Tobias Finis.
Weyl law with an error term for the cuspidal spectrum
14.05.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: