摘要
Let π△ be the automorphic representation of GL（2, QA） associated with Ramanujan modular form A and L（s, π△） the global L-function attached to π△. We study Selberg＇s integral for the automorphic L-function L（s, π△） under GRH. Our results give the information for the number of primes in short intervals attached to Ramanujan automorphic representation.
Let π△ be the automorphic representation of GL（2, QA） associated with Ramanujan modular form A and L（s, π△） the global L-function attached to π△. We study Selberg＇s integral for the automorphic L-function L（s, π△） under GRH. Our results give the information for the number of primes in short intervals attached to Ramanujan automorphic representation.
基金
Supported by National Natural Science Foundation of China （Grant No. 10571107）Acknowledgements The author expresses her thanks to Professor Jianya Liu and Professor Yangbo Ye for encouragernent, and to Professor Xiumin Ren for valuable suggestions. This work was completed when the author visited The University of Iowa supported by CSC. The author would like to thank Department of Mathematics, The University of Iowa for hospitality and support.
