Exponential moments of the logarithm of the Riemann zeta-function twisted by arguments

We discuss moments of the Riemann zeta-function in this paper. The purpose of this paper is to give an upper bound of exponential moments of the logarithm of the Riemann zeta-function twisted by arguments. Our results contain an improvement of Najnudel result for exponential moments of the argument of the Riemann zeta-function and an unconditional upper bound of the moments.