I am at the very beginning of a PhD which should be in complex analysis. Now I'm going to decide on what I should work on.
My question could be vague, but it couldn't be different.
I love the classic complex analysis in one variable, special functions, integral transforms, continued fractions (I know there exists a link between generalized continued fractions and holomorphic functions), Galois theory, Group theory, and something from Representation theory. Then here on MSE sometimes I see Lambert W function, polylogarithmic functions, digamma functions which are so sexy to me.
Can someone experienced suggest me some direction to follow? Some research topic? Some book/article to read? Some "slice" of Mathematics which embraces the pointed subjects?