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

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    $\begingroup$ 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... $\endgroup$ – Crostul Dec 30 '15 at 14:56

Any class that needs a working knowledge of complex analysis also requires a working knowledge of complex analysis, even if it is not explicitly stated.

Knowing how to add fractions is also not explicitly stated, but it is probably required...

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  • $\begingroup$ Because the "math for physics" book I have is completely self-contained and doesn't have any real analysis, but has a section on "complex variables" which got me wondering. The book is by riley, bence and hobson: esperia.iesl.forth.gr/~kafesaki/Applied-Mathematics/Riley.pdf $\endgroup$ – user45220 Dec 30 '15 at 15:05
  • $\begingroup$ @user45220 Complex variables $\neq$ complex analysis. Complex analysis includes things like complex integrals and holomorphic functions... $\endgroup$ – 5xum Dec 30 '15 at 15:06
  • $\begingroup$ Thanks, I guess that solves my problem then $\endgroup$ – user45220 Dec 30 '15 at 15:07
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    $\begingroup$ Sorry, I don't understand the first sentence: Any class that needs complex analysis also requires complex analysis, even if it is not explicitly stated ? $\endgroup$ – Dietrich Burde Dec 30 '15 at 15:41

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