The distribution of Fourier coefficients of symmetric square L-functions over arithmetic progressions

Let L(s, sym2 f) be the corresponding symmetric square L-function associated to f ( z), where f (z) is a primitive holomorphic cusp form of even integral weight k for the full modular group. Suppose that.sym2 f (n) is the nth normalized Fourier coefficient of L(s, sym2 f). In this paper, we use the function equation and the large sieve inequality to study the asymptotic behaviour of the sums nx n=a(mod q). j sym2 f (n), 2 j 4.