Theta constant
In mathematics, a theta constant or
Thetanullwert' is the restriction θm = θm of a theta function θm with rational characteristic m to z = 0. The variable τ may be a complex number in the upper half-plane in which case the theta constants are modular forms, or more generally may be an element of a Siegel upper half plane in which case the theta constants are Siegel [modular form]s. The theta [function of a lattice] is essentially a special case of a theta constant.
Definition
The theta function θm = θa,''bis defined bywhere n'' is a positive integer, called the genus or rank. m = is called the characteristica,''b are in Rn''τ is a complex n by n matrix with positive definite imaginary partz is in Cnt means the transpose of a row vector.
If a,''b are in Qn'' then θa,''b'' is called a theta constant.