Resurgent Theta-functions: a conjectured gateway into dimension D superior at 1 quantum mechanics Resurgent analysis of the stationary Schrödinger equation (exact-WKB method) has remained exclusivelyconfined to 1D systems due to its underlying linear-ODE techniques.Here, building on a solvable 2D case (a Selberg trace formula, as analyzed with P. CARTIER), and on a Balian-Bloch abstract quantum framework in any dimension using complex orbits, we isolate a very special generalized-heat-trace function as best candidate to start some resurgent description of quantum mechanics in general dimension. The latter statement is still quite embryonic and speculative - our main hope is to encourage future research.