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.

OriginalsprogEngelsk
TidsskriftMathematical Proceedings of the Cambridge Philosophical Society
Vol/bind172
Sider (fra-til)705–728
ISSN0305-0041
DOI
StatusUdgivet - 2022

Bibliografisk note

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

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