Given a complex function $f(z)=\displaystyle \int\frac{dz}{\sqrt{P(z)}}$, where $P(z)$ is a polynomial of $n$ degree, is it possible to affirm that this function always have Riemann surfaces separated by $2\pi i$?
So, it would be valid to express it as $f(z) + 2\pi i=\displaystyle \int\frac{dz}{\sqrt {P(z)}}$?
The numerical values are difficult to determine. In one of the simplest cases, in which $P(z)$ is a quadratic polynomial, the integral is called an.Elliptic integral The numerical values of the periods of that integral depend on the coefficients of the quadratic in a fashion that has been studied for centuries, notably by Gauss. See also the Schwarz-Christoffel mapping as an application. Schwarz-Christoffel mapping