t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-functio...t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-function associated with f(z), and Asym2f(n) de- notes the nth coefficient L(sym2f, s). In this paper, it is proved that where P2 (t) is a polynomial in t of degree 2. Similarly, it is obtained that where P2(t) is a polynomial in t of degree 2.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10971119,11101249)the Shandong Provincial Natural Science Foundation of China(No.ZR2009AQ007)
文摘t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-function associated with f(z), and Asym2f(n) de- notes the nth coefficient L(sym2f, s). In this paper, it is proved that where P2 (t) is a polynomial in t of degree 2. Similarly, it is obtained that where P2(t) is a polynomial in t of degree 2.