Theta Function - Generalizations

Generalizations

If F is a quadratic form in n variables, then the theta function associated with F is

with the sum extending over the lattice of integers Zn. This theta function is a modular form of weight n/2 (on an appropriately defined subgroup) of the modular group. In the Fourier expansion,

the numbers R_F(k) are called the representation numbers of the form.