非線形問題と複素幾何学
《非線形問題と複素幾何学》 · 第 360 页 · Section 14.3「Poincaré series」，Proposition 14.5
Taken together, the two previous lemmas imply a formula which shows how the sequences of Fourier coefficients of a basis of $S_k(q,\chi)$ are almost orthogonal, thereby giving another decomposition in arithmetic harmonics of the diagonal symbol $\delta(m,n)$. Taking the $n$th Fourier coefficient of both sides, we obtain the Petersson formula.