Dedekind eta function

The Dedekind eta function is a special mathematical function that arises in number theory and complex analysis. It is defined on the complex plane and encodes deep symmetries related to ways of partitioning integers and properties of modular forms. The eta function is constructed using an infinite product that converges and exhibits elegant transformation properties under certain geometric movements called modular transformations. These properties make it fundamental in understanding the structure of modular objects, with applications spanning from elliptic curves to theoretical physics, especially in string theory and conformal field theory.