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Hilbert modular forms of weight 1/2 and theta functions

Achimescu, Sever and Abhishek, Saha (2008) Hilbert modular forms of weight 1/2 and theta functions. Journal of Number Theory, 128 (12). pp. 3037-3062. ISSN 0022-314X. doi:10.1016/j.jnt.2008.04.001.

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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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Additional Information:© 2008 Elsevier Inc. Received 11 March 2008. Available online 9 June 2008. Communicated by James Cogdell. The authors wish to thank their advisor D. Ramakrishnan for guidance and helpful discussions.
Issue or Number:12
Record Number:CaltechAUTHORS:ACHjnt08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13149
Deposited By: Jason Perez
Deposited On:29 Jan 2009 22:12
Last Modified:08 Nov 2021 22:35

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