A holomorphic function f on the upper half-plane satisfying f((az+b)/(cz+d)) = (cz+d)^k f(z) for all (a,b;c,d) ∈ SL₂(ℤ) (or a congruence subgroup), plus growth at cusps. Fourier coefficients encode deep arithmetic.
A holomorphic function f on the upper half-plane satisfying f((az+b)/(cz+d)) = (cz+d)^k f(z) for all (a,b;c,d) ∈ SL₂(ℤ) (or a congruence subgroup), plus growth at cusps. Fourier coefficients encode deep arithmetic.