Laplacian - crowlogic/arb4j GitHub Wiki

The Laplacian on the Riemann surface associated with g(x) can be computed using the Riemann-Roch theorem and the theory of automorphic forms, as mentioned earlier. The Laplacian is a differential operator that acts on functions defined on the Riemann surface, and its eigenfunctions are automorphic forms associated with the Laplace-Beltrami operator. These eigenfunctions form a complete orthonormal basis for the space of automorphic forms, and their eigenvalues determine the spectrum of the Laplacian.