The distributions of coefficients of triple product L-functions over arithmetic progressions

Let f and g be two distinct normalized primitive holomorphic cusp forms of even integral weights k₁ and k₂ for the full modular group SL(2,Z), respectively. And let λf× f× f(n) and λf× f× g(n) denote the nth coefficients of triple product L-functions L(f× f× f,s) and L(f× f× g,s) associated to f and $f,g$, respectively. In this paper, we establish the asymptotic formulae for\[∑_{{n≤ x \\ n≡ l( q)}}λf× f× f²(n) and ∑_{{n≤ x \\ n≡ l( q)}}λf× f× g²(n)\]where q is a prime with $(l,q)=1$. And we also consider other similar results of the above types.