Estimates of the argument function of automorphic L-functions for GL(2)*

摘要

We study the argument of L(s, f) associated with holomorphic cusp form in both weight aspect and t-aspect. We prove that for -1 <= sigma <= 2 and t >= 4, argL(s, f) MUCH LESS-THAN log kt, where s = sigma + it. Assuming the generalized Riemann hypothesis (GRH), we have arg L(s, f) MUCH LESS-THAN log kt/log log kt for sigma >= 1/2 and t >= 4.