Complex analysis prerequisites for Silverman's The Arithmetic of Elliptic Curves

Question

I would like to take a course on elliptic curves using Silverman's The Arithmetic of Elliptic Curves next year. I would be taking complex analysis concurrently, but it was listed as a formal prerequisite, so I was planning to learn some complex analysis beforehand. What topics from complex analysis (esp. chapters from Stein's book) would I need to know to do elliptic curves over $\mathbb{C}$?

Answer 1

If you are referring to Stein's Complex Analysis (Princeton Lectures in Analysis, vol 2) by Elias M. Stein, Rami Shakarchi, then I'd suggest the following chapters/topics:

• Chapter 1: Preliminaries to Complex Analysis
• Chapter 2: Cauchy's Theorem
• Chapter 3: Meromorphic Functions and the Logarithm
• Chapter 5: Entire Functions
• Chapter 6: The Gamma and Zeta Functions
• Chapter 7: The Zeta Function and Prime Number Theorem
• Chapter 9: An Introduction to Elliptic Functions

Answer 2

To begin on this topic I highly recommend Lectures on Elliptic Curves, J. W. S. Cassels. London Mathematical Society. Student Texts 24. This book of Professor Cassels is indeed bright and decorated with a truly extraordinary didactic sense. You can get it free by internet.