A conditional construction of artin representations for real analytic siegel cusp forms of weight (2, 1)

Henry H. Kim, Takuya Yamauchi

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

Let F be a vector-valued real analytic Siegel cusp eigenform of weight (2, 1) with the eigenvalues −5/12 and 0 for the two generators of the center of the algebra consisting of all Sp4 (R)-invariant differential operators on the Siegel upper half plane of degree 2. Under natural assumptions in analogy of holomorphic Siegel cusp forms, we construct a unique symplectically odd Artin representation ρF: GQ − GSp4 (C) associated to F. For this, we develop the arithmetic theory of vector-valued real analytic Siegel modular forms. Several examples which satisfy these assumptions are given by using various transfers and automorphic induction.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages225-260
Number of pages36
DOIs
Publication statusPublished - 2016
Externally publishedYes

Publication series

NameContemporary Mathematics
Volume664
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Artin representation
  • Siegel modular forms

ASJC Scopus subject areas

  • Mathematics(all)

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