A bstract We study elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs from their modularity and explore the relation to topological string partition functions. find a novel kinematical constraint that should follow, which determines at low base degrees helps us conjecture vanishing bound for refined Gopakumar-Vafa invariants related geometries. Using this, we can bootstrap arbitrary degree...

A bstract The eigenvalues of the Laplace-Beltrami operator and integrals products eigenfunctions holomorphic s -differentials satisfy certain consistency conditions on closed hyperbolic surfaces. These can be derived by using spectral decompositions to write quadruple overlap in terms triple different ways. We show how efficiently construct these use them derive upper bounds eigenvalues, follow...