An improved upper bound for the argument of the Riemann zeta-function on the critical line II

TextThis paper concerns the function S(T)S(T), where πS(T)πS(T) is the argument of the Riemann zeta-function along the critical line. The main result is that|S(T)|⩽0.112logT+0.278loglogT+2.510,|S(T)|⩽0.112logT+0.278loglogT+2.510, which holds for all T⩾eT⩾e.VideoFor a video summary of this paper, please click here or visit http://youtu.be/FldP0idE0aI.