EXPONENTIAL-SUMS AND ROUNDING ERROR

Let F(x) be a real function with sufficiently many derivatives existing and satisfying certain non-vanishing conditions for 1 less-than-or-equal-to x less-than-or-equal-to 2. The rounding-error sum [GRAPHICS] where rho(t) is 1/2-t for 0 < t < 1, and has period one, can be estimated by exponential-sum methods. We give order of magnitude bounds; the numerical constants depend in a complicated way on the derivatives. Resonance can occur if certain derivatives are stationary with rational values.