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Monatshefte für Mathematik

, Volume 185, Issue 1, pp 17–41 | Cite as

Non-vanishing of automorphic L-functions of prime power level

Article
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Abstract

We prove that at the minimum \(25\%\) of L-values associated to holomorphic newforms of fixed even integral weight and large prime power level do not vanish at the critical point.

Keywords

L-functions Primitive forms Non-vanishing Prime power level 

Mathematics Subject Classification

Primary 11F12 

Notes

Acknowledgements

The authors thank the referee for careful reading and Sandro Bettin for extending his result [3] to the case of prime powers.

Compliance with ethical standards

Funding

The work of Olga Balkanova (Sects. 3 and 5) is supported by the Russian Science Foundation under Grant \(14-11-00335\) and performed in the Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch of Russian Academy of Sciences. The work of Dmitry Frolenkov (Sects. 4 and 6) is supported by the Russian Science Foundation under Grant \(14-50-00005\) and performed in Steklov Mathematical Institute of Russian Academy of Sciences.

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Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.Institute for Applied MathematicsFar Eastern Branch of the Russian Academy of SciencesKhabarovskRussia
  2. 2.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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