Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this ...Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,Mk（q,f）=∑χ（mod q）χ≠χ0｜L（1/2,f χ）｜^2k〈〈 kФ（q）（log q）^k^2, and the result also holds for any real number 0 〈 k 〈 1 under the GRH for L（s, f χ）.The authors also prove that under the GRH for L（s, f χ）,for any real number k 〉 0 and any large prime q.展开更多
基金supported by the National Natural Science Foundation of China(No.11301299)the Natural Science Foundation of Shandong Province(No.ZR2012AQ001)the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)(Nos.20110131120001,20120131120075)
文摘Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,Mk（q,f）=∑χ（mod q）χ≠χ0｜L（1/2,f χ）｜^2k〈〈 kФ（q）（log q）^k^2, and the result also holds for any real number 0 〈 k 〈 1 under the GRH for L（s, f χ）.The authors also prove that under the GRH for L（s, f χ）,for any real number k 〉 0 and any large prime q.
