Effective Weak Universality in Short Intervals

We prove an effective universality theorem of the Riemann zeta-function in short intervals $[T,T+H]$ with T27/82≤ H≤ T by following an effective multidimensional Ω-result of Voronin. Furthermore, we also prove the results in short intervals $[T,T+H]$ with T^ε≤ H≤ T (for any fixed ε>0) under the assumption of the Riemann Hypothesis.