In other words , it satisfies the elliptic partial differential equation
Viewed as a function of z , E ( z , s ) is a real - analytic eigenfunction of the Laplace operator on H with the eigenvalue s ( s - 1 ) .
It satisfies the elliptic partial differential equation
Viewed as a function of z , E ( z , s ) is a real - analytic eigenfunction of the Laplace operator on H with the eigenvalue s ( s - 1 ) .