An improved explicit bound on vertical bar zeta(1/2+it)vertical bar

作者：Platt D J; Trudgian T S^*

来源：Journal of Number Theory, 2015, 147: 842-851.

DOI：10.1016/j.jnt.2014.08.019

• Explicit bounds
• Riemann zeta-function
• Exponential sums

This article proves the bound vertical bar zeta(1/2 + it)vertical bar <= 0.732t (1/6) log t for t >= 2, which improves on a result by Cheng and Graham. We also show that vertical bar zeta(1/2 + it)vertical bar <= 0.732 vertical bar 4.678 + it vertical bar(1/6) log vertical bar 4.678 + it vertical bar for all t.

• 出版日期2015-2