, Volume 110, Issue 2, pp 251-272

Graded rings of Hermitian modular forms of degree 2

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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.

Received: 26 February 2002 Published online: 24 January 2003
Dedicated to Professor Dr. Helmut Klingen on the occasion of his 75th birthday
Mathematics Subject Classification (2000): 11F55, 11F27