The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\) (Q1323452)
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scientific article; zbMATH DE number 567449
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\) |
scientific article; zbMATH DE number 567449 |
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The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\) (English)
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30 May 1994
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We determine the zeros of the theta functions (defined and holomorphic on the upper halfplane) \(\theta(z)= \sum_{x,y\in\mathbb{Z}[i]} e^{\pi i{\mathbf Q}(x,y)z}\), and of related functions, \(Q\) any positive binary-Hermitian form over \(\mathbb{Z}[i]\). In particular we show that all these zeros are Heegner-points.
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zeros of theta functions
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binary-Hermitian form
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Heegner-points
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