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Triple correlations of Fourier coefficients of cusp forms (1607.02956v1)
Published 11 Jul 2016 in math.NT
Abstract: 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 $\sum_{H\leq h\leq 2H}W\big(\frac{h}{H}\big)\sum_{X\leq n\leq 2X}\lambda_{1}(n-h)\lambda_{2}(n)\lambda_{3}(n+h)$, which is nontrivial provided that $H\geq X{2/3+\varepsilon}$. The result can be viewed as a cuspidal analogue of a recent result of Blomer on triple correlations of divisor functions.
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