Triple correlations of Fourier coefficients of cusp forms.

We treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms. As a consequence, we obtain an upper bound for correlation of three Hecke eigenvalues of holomorphic cusp forms ∑H≤h≤2HWhH∑X≤n≤2Xλ1(n-h)λ2(n)λ3(n+h)<inline-graphic></inline-graphic>, which is nontrivial provided that H≥X2/3+ε<inline-graphic></inline-graphic>. The result can be viewed as a cuspidal analogue of a recent result of Blomer on triple correlations of divisor functions. [ABSTRACT FROM AUTHOR]