# Analysis needed for analytic number theory?

I was reading the prerequisites for an analytic number theory course and to my surprise the only prerequisite was "working knowledge of complex analysis". I took this to mean "complex analysis for physicists", because there is a complex analysis chapter in my "math for physicists" book which just says "functions of a complex variable".

My question is: Does this mean I don't need real analysis either? Because if you think about it, to get a working knowledge of complex analysis you only need a working knowledge of analysis (that is, calculus), so analysis ends up being not needed.

I always thought analytic number theory had a deep connection with analysis.

Any clarification would be appreciated.

Note: The course I am referring to can be found here (it is quite old, but the instructor is "Ben Green" himself): http://web.archive.org/web/20070708001729/http://www.math.cam.ac.uk/postgrad/casm/descriptions.pdf

• How is it possible to have knowledge of complex analysis without knowing real analysis? It would be something like knowing rational numbers without knowing natural numbers... – Crostul Dec 30 '15 at 14:56

• @user45220 Complex variables $\neq$ complex analysis. Complex analysis includes things like complex integrals and holomorphic functions... – 5xum Dec 30 '15 at 15:06