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Forum Mathematicum

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Volume 28, Issue 5

Issues

Vector valued theta functions associated with binary quadratic forms

Stephan EhlenORCID iD: http://orcid.org/0000-0003-2029-6219
Published Online: 2015-10-14 | DOI: https://doi.org/10.1515/forum-2015-0034

Abstract

We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta functions of weight one and determine an orthogonal basis with respect to the Petersson inner product. Moreover, we give an explicit formula for the Petersson norms of the elements of this basis.

Keywords: Theta functions; binary quadratic forms; CM values

MSC 2010: 11F11; 11F27; 11E16

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About the article


Received: 2015-02-17

Revised: 2015-07-25

Published Online: 2015-10-14

Published in Print: 2016-09-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: BR-2163/2-1

This work was partly supported by DFG grant BR-2163/2-1.


Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 893–908, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0034.

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