Non-vanishing of special $L$ -values of cusp forms on GL(2) with totally split prime power twists

preprint2021arXivOpen access

We prove the non-vanishing of special $L$ -values of cuspidal automorphic forms on GL(2) twisted by Hecke characters of prime power orders and totally split prime power conductors. Main ingredients of the proof are estimating the Galois averages of fast convergent series expressions of special $L$ -values and considering Shintani cone decomposition.

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Non-vanishing of special $L$ -values of cusp forms on GL(2) with totally split prime power twists

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Non-vanishing of special LLL-values of cusp forms on GL(2) with totally split prime power twists

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Non-vanishing of special $L$ -values of cusp forms on GL(2) with totally split prime power twists