EXPONENTIAL MOMENTS OF THE ARGUMENT OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE

摘要

In this article, we give, under the Riemann hypothesis, an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line. Our result, which gives information on the fluctuations of the distribution of the zeros of zeta, has the same accuracy as the result obtained by Soundararajan (Ann. of Math. (2)170(2) (2009), 981-993) for the moments of |zeta|.