Petersson trace formula


In analytic number theory, the Petersson trace formula is a kind of orthogonality relation between coefficients of a holomorphic modular form. It is a specialization of the more general Kuznetsov trace formula.
In its simplest form the Petersson trace formula is as follows. Let be an orthonormal basis of, the space of cusp forms of weight on. Then for any positive integers we have
where is the Kronecker delta function, is the Kloosterman sum and is the Bessel function of the first kind.