Vector valued theta functions associated with binary quadratic forms
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Stephan Ehlen
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.
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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© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- On the K-theory of certain extensions of free groups
- Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators
- Regular subspaces of skew product diffusions
- Singular values and evenness symmetry in random matrix theory
- Vector valued theta functions associated with binary quadratic forms
- Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V
- Annelidan rings
- Brieskorn manifolds, positive Sasakian geometry, and contact topology
- Symplectic Lefschetz fibrations on adjoint orbits
- The hyperbolic lattice point problem in conjugacy classes
- Corrigendum to: Algebraic supergroups of Cartan type
- Corrigendum to: Separable ultrametric spaces and their isometry groups
Artikel in diesem Heft
- Frontmatter
- On the K-theory of certain extensions of free groups
- Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators
- Regular subspaces of skew product diffusions
- Singular values and evenness symmetry in random matrix theory
- Vector valued theta functions associated with binary quadratic forms
- Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V
- Annelidan rings
- Brieskorn manifolds, positive Sasakian geometry, and contact topology
- Symplectic Lefschetz fibrations on adjoint orbits
- The hyperbolic lattice point problem in conjugacy classes
- Corrigendum to: Algebraic supergroups of Cartan type
- Corrigendum to: Separable ultrametric spaces and their isometry groups
