On the Non-vanishing of the Central Value of Certain L-functions: Unitary Groups

Jiang, Dihua; Zhang, Lei

doi:10.48550/arxiv.1806.04340

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“…While Shahidi's approach might be adaptable to our setting, we have not attempted that route. In yet another direction, using the theory of endoscopy, D. Jiang and L. Zhang have recently proved related nonvanishing results under certain conditions in [JZ18].…”

Section: Introductionmentioning

confidence: 99%

Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$-functions

Eischen

2017

Preprint

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We prove the nonvanishing of the twisted central critical values of a class of automorphic L-functions for twists by all but finitely many unitary characters in particular infinite families. While this paper focuses on L-functions associated to certain automorphic representations of unitary groups, it illustrates how decades-old nonarchimedean methods from Iwasawa theory can be combined with the output of new machinery to achieve broader nonvanishing results. In an appendix, which concerns an intermediate step, we also outline how to extend relevant prior computations for p-adic Eisenstein series and L-functions on unitary groups to the case where primes dividing p merely needs to be unramified (whereas prior constructions required p to split completely) in the associated reflex field.

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Section: Introductionmentioning

confidence: 99%

Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$-functions

Eischen

2017

Preprint

View full text Add to dashboard Cite

show abstract

On the Non-vanishing of the Central Value of Certain L-functions: Unitary Groups

Cited by 1 publication

References 12 publications

Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$-functions

Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$-functions

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