A ZERO-FREE REGION FOR THE FRACTIONAL DERIVATIVES OF THE RIEMANN ZETA FUNCTION.

For any α 2 R, we denote by D s (s)] the -th Grunwald-Letnikov fractional derivative of the Riemann zeta function (s). For these derivatives we show: ... inside the region |s - 1| < 1. This result, the first of its kind, is proved by a careful analysis of integrals involving Bernoulli polynomials and bounds for fractional Stieltjes constants. [ABSTRACT FROM AUTHOR]