André Voros - Simplification of the Keiper--Li approach to the Riemann Hypothesis
We review Keiper and Li's constants \lambda_n, n=1,2, ..., real numbers whose large n behavior sharply reflects whether the Riemann Hypothesis (RH) is true or not - a key open question in number theory. That sequence generates conceptually most concrete and practical tests for RH (thus, appealing for physicists): the prime example is Li's criterion. On the dark side, those numbers have a very elusive nature, and also numerically they become intractable at quite early n. Our analysis, partly semiclassical, makes the Keiper/Li approach more explicit and easier to implement numerically.
