Prime geodesics and averages of the Zagier L-series

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The Zagier L-series encode data of real quadratic fields. We study the average size of these L-series, and prove asymptotic expansions and omega results for the expansion. We then show how the error term in the asymptotic expansion can be used to obtain error terms in the prime geodesic theorem.

Original languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
Pages (from-to)705–728
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.

    Research areas

  • 11F72, 11M36, 11M41, 2020 Mathematics Subject Classification:

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