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Monatsh. Math., 2018, Volume 185, Issue 1, Pages 17–41 (Mi monm2)  

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

Olga Balkanovaa, Dmitry Frolenkovb

a Institute for Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00335
14-50-00005
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.


DOI: https://doi.org/10.1007/s00605-017-1031-4


Bibliographic databases:

ArXiv: 1605.02434
Document Type: Article
Received: 16.08.2016
Accepted:21.02.2017
Language: English

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