Hilbert modular forms of weight 1/2 and theta functions

Details Hilbert modular forms of weight 1/2 and theta functions Hilbert modular forms of weight 1/2 and theta functions

2008-03-26

arxiv.org/abs/0803.3788v1

Journal of Number Theory, Volume 128, Issue 12, December 2008, Pages 3037-3062

Mathematics

Number Theory

23 pages

Scientific paper

10.1016/j.jnt.2008.04.001

Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result - under certain mild restrictions on the level and character - to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical difficulties which arise when we move out of Q.

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