Let L（s, sym2f） be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL（2, Z）, with tf（n, 1） denoting the nthcoefficient of the Dirichlet series for it. It is proved that, for...Let L（s, sym2f） be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL（2, Z）, with tf（n, 1） denoting the nthcoefficient of the Dirichlet series for it. It is proved that, forN≥2and anyα∈ there exists an effective positive constant c such that ∑n≤N∧（n）tf（n,1）e（nα）〈〈N exp （-c√logN,where ∧（n） is the von Mangoldt function, and the implied constant only depends on f. We also study the analogue of Vinogradov＇s three primes theorem associated to the coefficients of Rankin-Selberg L-functions.展开更多
文摘Let L（s, sym2f） be the symmetric-square L-function associated to a primitive holomorphic cusp form f for SL（2, Z）, with tf（n, 1） denoting the nthcoefficient of the Dirichlet series for it. It is proved that, forN≥2and anyα∈ there exists an effective positive constant c such that ∑n≤N∧（n）tf（n,1）e（nα）〈〈N exp （-c√logN,where ∧（n） is the von Mangoldt function, and the implied constant only depends on f. We also study the analogue of Vinogradov＇s three primes theorem associated to the coefficients of Rankin-Selberg L-functions.
