# Fungrim entry: 154c44

$\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \theta_{1}\!\left(z , \tau\right) = \left\{ m + n \tau : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}$
Assumptions:$\tau \in \mathbb{H}$
TeX:
\mathop{\operatorname{zeros}\,}\limits_{z \in \mathbb{C}} \theta_{1}\!\left(z , \tau\right) = \left\{ m + n \tau : m \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, n \in \mathbb{Z} \right\}

\tau \in \mathbb{H}
Definitions:
Fungrim symbol Notation Short description
Zeros$\mathop{\operatorname{zeros}\,}\limits_{P\left(x\right)} f\!\left(x\right)$ Zeros (roots) of function
JacobiTheta$\theta_{j}\!\left(z , \tau\right)$ Jacobi theta function
CC$\mathbb{C}$ Complex numbers
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
ZZ$\mathbb{Z}$ Integers
HH$\mathbb{H}$ Upper complex half-plane
Source code for this entry:
Entry(ID("154c44"),
Formula(Equal(Zeros(JacobiTheta(1, z, tau), z, Element(z, CC)), SetBuilder(Add(m, Mul(n, tau)), Tuple(m, n), And(Element(m, ZZ), Element(n, ZZ))))),
Variables(tau),
Assumptions(Element(tau, HH)))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC