Monatsh. Math., 2018, Volume 185, Issue 1, Pages 17–41
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
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.
|Russian Science Foundation
|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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