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Prime geodesics and averages of the Zagier L-series
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2021-05-11 , DOI: 10.1017/s0305004121000384 OLGA BALKANOVA 1 , DMITRY FROLENKOV 2 , MORTEN S. RISAGER 3
中文翻译:
Zagier L 系列的主要测地线和平均值
更新日期:2021-05-11
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2021-05-11 , DOI: 10.1017/s0305004121000384 OLGA BALKANOVA 1 , DMITRY FROLENKOV 2 , MORTEN S. RISAGER 3
Affiliation
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.
中文翻译:
Zagier L 系列的主要测地线和平均值
Zagier L系列对实数二次场的数据进行编码。我们研究了这些L系列的平均大小,并证明了渐近扩展和扩展的 omega 结果。然后,我们展示了如何使用渐近展开中的误差项来获得素测地线定理中的误差项。