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 language | English |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
Volume | 172 |
Pages (from-to) | 705–728 |
ISSN | 0305-0041 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society.
- 11F72, 11M36, 11M41, 2020 Mathematics Subject Classification:
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