An explicit hybrid estimate for $L(1/2+it,\chi )$
Volume 176 / 2016
Acta Arithmetica 176 (2016), 211-239 MSC: Primary 11M06, 11L40. DOI: 10.4064/aa8433-7-2016 Published online: 17 October 2016
An explicit hybrid estimate for $L(1/2+it,\chi )$ is derived, where $\chi $ is a Dirichlet character modulo $q$. The estimate applies when $t$ is bounded away from zero, and is most effective when $q$ is powerfull, yielding an explicit Weyl bound in this case. The estimate takes a particularly simple form if $q$ is a sixth power. Several hybrid lemmas of van der Corput–Weyl type are presented.