manuscripta mathematica

, Volume 110, Issue 2, pp 251–272

Graded rings of Hermitian modular forms of degree 2

Authors

  • Tobias Dern
    • Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany. e-mail: dern@mathA.rwth-aachen.de
  • Aloys Krieg
    • Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany. e-mail: krieg@mathA.rwth-aachen.de

DOI: 10.1007/s00229-002-0339-z

Cite this article as:
Dern, T. & Krieg, A. Manuscripta Math. (2003) 110: 251. doi:10.1007/s00229-002-0339-z

Abstract

 At first it is shown that any Siegel modular form of degree 2 and even weight can be lifted to a Hermitian modular form of degree 2 over any imaginary-quadratic number field K. In the cases \(\) and \(\) we describe the graded rings of Hermitian modular forms with respect to all abelian characters. Generators are constructed as Maaßlifts or as Borcherds products. The description allows a characterization in terms of generators and relations. Moreover we show that the graded rings are generated by theta constants by analyzing the associated five-dimensional representation of PSp2(ℤ/3ℤ). As an application the fields of Hermitian modular functions are determined.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002