# Computing complex zeros of polynomials and power series

# Computing complex zeros of polynomials and power series

The purpose of this chapter is twofold. First, it will prove two theorems (5.3.1 and 5.4.2) about the complexity of computing complex roots of polynomials and zeros of power series. The existence of a deterministic polynomial time algorithm for these purposes plays an important role in this book. More important, it will also explain what it means to compute with real or complex data in polynomial time. The chapter first recalls basic definitions in computational complexity theory, it then deals with the problem of computing square roots. The more general problem of computing complex roots of polynomials is treated thereafter and, finally, the chapter studies the problem of finding zeros of a converging power series.

*Keywords:*
modular forms, polynomials, complex roots, polynomial time, power series, square root

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.