Gold 66

Theta function of a lattice

Gold ID

66

Link

https://sigir21.wmflabs.org/wiki/Theta_function_of_a_lattice#math.118.0

Formula

${\mathrm{\Theta }}_{\mathrm{\Lambda }}(\tau )=\sum _{x\in \mathrm{\Lambda }}{e}^{i\pi \tau \Vert x{\Vert }^2}\mathrm{I}\mathrm{m}\tau >0$

TeX Source

\Theta_\Lambda(\tau) = \sum_{x\in\Lambda}e^{i\pi\tau\|x\|^2}\qquad\mathrm{Im}\,\tau > 0

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

\Theta_\Lambda(\tau) = \sum_{x\in\Lambda} \expe^{\iunit \cpi \tau \|x \|^2} \qquad \mathrm{Im} \tau > 0

Expected (Gold Entry)

\Theta_\Lambda(\tau) = \sum_{x\in\Lambda} \expe^{\iunit \cpi \tau \|x \|^2} \qquad \imagpart \tau > 0

Mathematica

Translation

Expected (Gold Entry)

\[CapitalTheta][\[CapitalLambda]_, \[Tau]_] := Sum[Exp[I*Pi*\[Tau]*(Norm[x])^(2)], {x, \[CapitalLambda]}]

Maple

Translation

Expected (Gold Entry)