AN IMPROVED UPPER BOUND FOR THE ARGUMENT OF THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE

作者：Trudgian Timothy^*

来源：Mathematics of Computation, 2012, 81(278): 1053-1061.

• Riemann zeta-function
• convexity estimate

This paper concerns the function S(t), the argument of the Riemann zeta-function along the critical line. Improving on the method of Backlund, and taking into account the refinements of Rosser and McCurley it is proved that for sufficiently large t, %26lt;br%26gt;vertical bar S(t)vertical bar %26lt;= 0.1013 log t. %26lt;br%26gt;Theorem 2 makes the above result explicit, viz, it enables one to select values of a and b such that, for t %26gt; t(0), %26lt;br%26gt;vertical bar S(t)vertical bar %26lt;= a + b log t.

• 出版日期2012-4