The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\)
type: Item
instance of: scholarly article
title: The zeros of theta functions belonging to binary-Hermitian forms over \(\mathbb{Z}[i]\)
zbMATH Open document ID: 0790.11035
DOI: 10.1007/BF02572412
published in: Mathematische Zeitschrift
publication date: 1994-05-30T00:00:00Z
full work available at URL: https://eudml.org/doc/174576
review text: 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.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 14J20
zbMATH DE Number: 567449
zbMATH Keywords: zeros of theta functions
zbMATH Keywords: binary-Hermitian form
zbMATH Keywords: Heegner-points
author: Carl Friedrich Hermann
MaRDI profile type: Publication
cites work: Q3863951
cites work: Q5535672
cites work: Heegner points and derivatives of \(L\)-series
cites work: Die Nullstellen der Thetareihen zu positiven, binär-quadratischen Formen. (Zeros of theta series for positive binary quadratic forms)
cites work: Q4771024
cites work: Q4039833
description: scientific article; zbMATH DE number 567449