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Prime geodesics and averages of the Zagier L-series

Mathematical Proceedings of the Cambridge Philosophical Society. 2022. Vol. 172. No. 3. P. 705–728.
Balkanova O., Frolenkov D., Risager M.

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.

Research target: Mathematics
Language: English
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DOI
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Keywords: Zagier L-seriesL-ряд Загье
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