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arXiv · 0803.3788

Hilbert modular forms of weight 1/2 and theta functions

Sever Achimescu·Abhishek Saha
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Abstract

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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Sever Achimescu, Abhishek Saha. 2008-03-26. Hilbert modular forms of weight 1/2 and theta functions. https://doi.org/10.1016/j.jnt.2008.04.001

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