ON HIGHER MOMENTS OF HECKE EIGENVALUES ATTACHED TO CUSP FORMS

Let f, g and h be three distinct primitive holomorphic cusp forms of even integral weights k(1), k(2) and k(3) for the full modular group Gamma = SL(2, Z), respectively, and let lambda(f)(n), lambda(g)(n) and lambda(h)(n) denote the nth normalized Fourier coefficients of f, g and h, respectively. We consider the cancellations of sums related to arithmetic functions lambda(g)(n), lambda(h)(n) twisted by lambda(f)(n) and establish the following results: Sigma(n <= x)lambda(f)(n)lambda(g)(n)(i)lambda(h)(n)(j) << (f,g,h,epsilon) x(1-1/2i+j + epsilon) for any epsilon > 0, where 1 <= i <= 2, i >= 5 are any fixed positive integers.