Non-vanishing of Miyawaki type lifts

Henry H. Kim, Takuya Yamauchi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the non-vanishing of the Miyawaki type lift in various situations. In the case of 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≡ 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 292.

Original languageEnglish
Pages (from-to)117-134
Number of pages18
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume89
Issue number2
DOIs
Publication statusPublished - 2019 Oct 1

Keywords

  • Langlands functoriality
  • Miyawaki type lift

ASJC Scopus subject areas

  • Mathematics(all)

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