3 problems

Perturbed-grid quadrature conjecture. For every continuous function $f$ and every $\alpha<1/2$,

Rate-exponent conjecture. Based on numerical experiments, it is conjectured that $4\alpha$ can be replaced by $2\alpha$ in the rate estimate for $|I-\tilde I_N|$ and…

Smoothness conjecture. It is conjectured that having $2\alpha$ derivatives, in the stated Hölder-continuity sense, is sufficient for convergence of the perturbed trigonometric inte…