A modest improvement on the function S ( T )
نویسنده
چکیده
This paper concerns the function S(T ), the argument of the Riemann zeta-function. Improving on the method of Backlund, and taking into account the refinements of Rosser and McCurley it is hereunder proved that for sufficiently large T |S(T )| ≤ 0.1013 log T. Theorem 2 makes the above result explicit, viz. it enables one to select values of a and b such that, for T > T0, |S(T )| ≤ a + b log T.
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