Riemann Theta Function

Let the Imaginary Part of a $g\times g$ Matrix ${\hbox{\sf F}}$ be Positive Definite, and ${\bf m}= (m_1,\ldots,m_g)$ be a row Vector with coefficients in $\Bbb{Z}$. Then the Riemann theta function is defined by

$$\vartheta(u)=\sum_{\bf m} \mathop{\rm exp}\nolimits [2\pi i(... ...\rm T}u+{\textstyle{1\over 2}}{\hbox{\sf F}}^{\rm T}{\bf m})].$$

See also Ramanujan Theta Functions, Theta Function

References

Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 9, 1980.