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A converse theorem for Jacobi cusp forms of degree two

Volume 189 / 2019

Winfried Kohnen, Yves Martin, Karam Deo Shankhadhar Acta Arithmetica 189 (2019), 223-262 MSC: Primary 11F50; Secondary 11F46, 11F37. DOI: 10.4064/aa180402-11-7 Published online: 12 April 2019

Abstract

We establish a converse theorem for Jacobi cusp forms of degree two. The methods combine and generalize arguments given in works of Imai, Arakawa–Makino–Sato and Martin to a vectorial setting, and they are presented in a detailed manner. As an application we obtain a converse theorem for half-integral weight Siegel cusp forms of degree 2 in Kohnen’s plus space.

Authors

  • Winfried KohnenMathematisches Institut
    Universität Heidelberg
    Im Neuenheimer Feld 205
    69120 Heidelberg, Germany
    e-mail
  • Yves MartinDepartamento de Matemáticas
    Facultad de Ciencias
    Universidad de Chile
    Las Palmera 3225
    Ñuñoa 7800003, Santiago, Chile
    e-mail
  • Karam Deo ShankhadharDepartment of Mathematics
    Indian Institute of Science Education and Research Bhopal
    Bhopal Bypass Road
    Bhauri, Bhopal 462066, Madhya Pradesh, India
    e-mail

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