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An explicit hybrid estimate for $L(1/2+it,\chi )$

Volume 176 / 2016

Ghaith A. Hiary 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.


  • Ghaith A. HiaryDepartment of Mathematics
    The Ohio State University
    231 West 18th Ave.
    Columbus, OH 43210, U.S.A.

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