arXiv subjects
Publications and source records attributed to Saeree Wananiyakul.
We prove an effective universality theorem of the Riemann zeta-function in short intervals $[T,T+H]$ with $T^{\frac{27}{82}}\le H\le T$ by following an effective multidimensional $Ω$-result of Voronin. Furthermore, we also prove the results in short intervals $[T,T+H]$ with $T^ε\le H\le T$ (for any fixed $ε>0$) under the assumption of the Riemann Hypothesis.
We improve a recent universality theorem for the Riemann zeta-function in short intervals due to Antanas Laurinčikas with respect to the length of these intervals. Moreover, we prove that the shifts can even have exponential growth. This research was initiated by two questions proposed by Laurin\v cikas in a problem session of a recent workshop on universality.
We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.