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Licensed Unlicensed Requires Authentication Published by De Gruyter October 14, 2015

Vector valued theta functions associated with binary quadratic forms

Stephan Ehlen ORCID logo
From the journal Forum Mathematicum

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.

MSC 2010: 11F11; 11F27; 11E16

Communicated by Jan Bruinier


Funding source: Deutsche Forschungsgemeinschaft

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

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

The results of this article are also contained in the author’s thesis [8]. I would like to thank my advisor Jan Bruinier for his constant support and helpful comments on an earlier version of this paper. Moreover, I thank the anonymous referee for carefully reading the manuscript and providing helpful comments.

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Received: 2015-2-17
Revised: 2015-7-25
Published Online: 2015-10-14
Published in Print: 2016-9-1

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