The idea of automorphic forms as analogous to symmetric colorings of a tesselation that shrinks on the boundary is a way more intuitive description than the mat

The idea of automorphic forms as analogous to symmetric colorings of a tesselation that shrinks on the boundary is a way more intuitive description than the mathematical definition of automorphic forms. So yes, I do feel like I know more about them from that definition versus the definition of invariance under subgroup action. And for the second quote, I took it to mean that the subset of automorphic forms that map to Diophantine equations can be used to generate an infinite sequence that maps to quantum energy levels which I believe means maps to the number of electrons in the orbit of the nucleus (2, 8, 18,...) etc.