What is the early history of the Dedekind eta function? In particular, why is it called the Dedekind eta function? Ramanujan's paper on the 24th power of the Dedekind eta function had appeared by 1916 and I have a reasonably good understanding what happened after that, in the other direction I know that by 1775 Euler had consider the Dedekind eta function divided by q^1/24 in his work which led to the pentagonal number theorem, but what happened between Euler and Ramanujan that led to the introduction of the factor of q^1/24 (which gives a half integer weight modular form) and the attachment of Dedekind's name to it?