A note on S(t) and the zeros of the Riemann zeta-function - Goldston, D. A.; Gonek, S. M. (The Bulletin of the London Mathematical Society, 2007)
Let π S(t) denote the argument of the Riemann zeta-function at the point 1/2 + it. Assuming the Riemann hypothesis, we sharpen the constant in the best currently known bounds for S(t) and for the change of S(t) in intervals. We then deduce estimates for the largest multiplicity of a zero of the zeta-function, and for the largest gap between the zeros.