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  Non-vanishing of Miyawaki type lifts

Kim, H. H., & Yamauchi, T. (2019). Non-vanishing of Miyawaki type lifts. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 89(2), 117-134. doi:10.1007/s12188-019-00207-6.

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 Creators:
Kim, Henry H.1, Author           
Yamauchi, Takuya1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case of ${\rm GSpin}(2,10)$ constructed in Kim and Yamauchi (Math Z 288(1–2):415–437, 2018), we use the fact that the Fourier coefficient at the identity is closely related to the Rankin–Selberg L-function of two elliptic cusp forms. In the case of the original Miyawaki lifts of Siegel cusp forms, we use the fact that certain Fourier coefficients are the Petersson inner product which is non-trivial. This provides infinitely many examples of non-zero Miyawaki lifts. We give explicit examples of degree 24 and weight 24. We also prove a similar result for Miyawaki lifts for unitary groups. Especially, we obtain an unconditional result on non-vanishing of Miyawaki lifts for $U(n+1,n+1)$ for each $n\equiv 3$ mod 4. In the last section, we prove the non-vanishing of the Miyawaki lifts for infinitely many half-integral weight Siegel cusp forms. We give explicit examples of degree 16 and weight $\frac{29}{2}$.




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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 18
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 Rev. Type: Peer
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Title: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
  Abbreviation : Abh. Math. Semin. Univ. Hambg.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 89 (2) Sequence Number: - Start / End Page: 117 - 134 Identifier: -