Complex analysis prerequisites for Silverman's The Arithmetic of Elliptic Curves 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 $\mathbb{C}$?

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:


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*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

