Cusp forms on the exceptional group of type E7

Henry H. Kim, Takuya Yamauchi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Let G be the connected reductive group of type E7,3 over ℚ and L be the corresponding symmetric domain in ℂ27. Let τ = G(ℤ) be the arithmetic subgroup de ned by Baily. In this paper, for any positive integer k ≥ 10, we will construct a (non-zero) holomorphic cusp form on L of weight 2k with respect to τ from a Hecke cusp form in S2k-8(SL2(ℤ)). We follow Ikeda's idea of using Siegel's Eisenstein series, their Fourier{Jacobi expansions, and the compatible family of Eisenstein series.

Original languageEnglish
Pages (from-to)223-254
Number of pages32
JournalCompositio Mathematica
Volume152
Issue number2
DOIs
Publication statusPublished - 2016 Feb 1
Externally publishedYes

Keywords

  • Eisenstein series
  • Exceptional group of type E
  • Ikeda lift
  • Langlands functoriality

ASJC Scopus subject areas

  • Algebra and Number Theory

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