Complex analysis in theoretical computer science There are many applications of real analysis in theoretical computer science, covering property testing, communication complexity, PAC learning, and many other fields of research. However, I can't think of any result in TCS that relies on complex analysis (outside of quantum computing, where complex numbers are intrinsic in the model). Does anyone has an example of a classical TCS result that uses complex analysis?
It's not a single problem, but the entire field of analytic combinatorics (see the book by Flajolet and Sedgewick) explores how to analyze the combinatorial complexity of counting structures (or even algorithm running times) by writing down an appropriate generating function and analyzing the structure of the complex solutions.