Central subject of this thesis are so called elliptic functions. Elliptic functions are a special type of meromorphic functions (complex-valued functions in one complex variable, which are holomorphic apart from a discrete set of poles) that are periodic in two directions on the complex plane, i.e. $ f(x) = f(x+a) $ and $ f(x) = f(x+b) $ for any $ x $ out of the domain with two complex numbers $ a $ and $ b $ (which are required to be non-collinear on the complex plane).
Among others, elliptic functions are of great use in number theory, in particular there are interesting connections to sums of divisors of natural numbers. Furthermore they are used in the theory of elliptic curves and elliptic integrals.
Subject of the thesis are so called elliptic functions, meromorphic functions that are periodic in two directions, i.e. invariant under a translation of their argument by two linearly independent complex numbers.
Among others, elliptic functions are of great use in number theory, in particular there are interesting connections to sums of divisors of natural numbers. Furthermore they are used in the theory of elliptic curves and elliptic integrals.
Imaginary part of the Weierstrass p function, an example of an elliptic function. Clearly visible are the two periods $ p(x+2) = p(x) = p(x+2i) $ throughout the domain.