A note on sums of powers which have a fixed number of prime factors.
Let be a normalized primitive holomorphic cusp form of even integral weight for the full modular group , and denote its th Fourier coefficient by . We consider the hybrid problem of quadratic forms with prime variables and Hecke eigenvalues of normalized primitive holomorphic cusp forms, which generalizes the result of D. Y. Zhang, Y. N. Wang (2017).