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What puts the analysis in analytic number theory?

  1. Aug 14, 2011 #1
    I'm interested in analytic number theory and from what little I understand of it complex analysis will be more important than real analysis(measure theory). Thus I will be taking a year of graduate complex analysis this fall, however, I do also have the option of taking a year of graduate real analysis, but I would prefer not to for several reasons, so I was hoping someone could enlighten me on if a lot of measure theory and highbrow function space theory is really even that useful in analytic number theory, or if I can be content with tools drawn primarily from complex analysis and abstract algebra.

    Edit: I guess I should clarify I will eventually get around to learning the topics covered in a standard graduate real analysis course, it just wont be right away, and I'm sure some of it will be crucial, I guess what I'm really asking is what types of analysis are the analytic number theorists finding to be their bread and butter.
    Last edited: Aug 14, 2011
  2. jcsd
  3. Aug 18, 2011 #2
    Complex analysis would be a better choice as it finds more applications in analytic number theory than the 'functional analysis' type.
  4. Aug 18, 2011 #3


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    it depends what you try to read. possibly as an extreme example, andre weil uses haar measure on page one of his book "Basic number theory".
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