Oscillations of coefficients of symmetric square L-functions over primes  

作　　者：Fei HOU 

机构地区：[1]School of Mathematics, Shandong University, Jinan 250100, China

出　　处：《Frontiers of Mathematics in China》2015年第6期1325-1341,共17页中国高等学校学术文摘·数学（英文）

摘　　要：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.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.

关 键 词：symmetric-square L-function primitive holomorphic cusp form Fourier coefficient 

分 类 号：O156.4[理学—数学] O174[理学—基础数学]