A theta constant is a value of a theta function at zero argument. For a symmetric 
complex matrix 
whose imaginary
part is positive definite, and column vectors 
and 
with entries 0 or 
, a theta constant with half-integer
characteristic is
 |
where 
denotes the transpose (NIST DLMF, §21.2). The
zero characteristic gives 
for the Riemann
theta function. Umemura's formula uses theta
constants to express polynomial roots.
