Ah, so you've heard of the Riemann zeta function, have you not, and no doubt you will want to start programming with it, yes? If so, read on!
To know it in its contemporary form, you should have a basic knowledge of complex analysis, including Cauchy's theorem and contour integration. (Note that Euler studied this function earlier without complex analysis but his analysis was limited to the R-z as a function of real variable, rather than a complex variable).
A flavour of the subject can be found here and here (the latter addresses analytic number theory under the headline of multiplicative number theory). Prepare to be dazzled by the spectral theory of automorphic forms.
To know it in its contemporary form, you should have a basic knowledge of complex analysis, including Cauchy's theorem and contour integration. (Note that Euler studied this function earlier without complex analysis but his analysis was limited to the R-z as a function of real variable, rather than a complex variable).
A flavour of the subject can be found here and here (the latter addresses analytic number theory under the headline of multiplicative number theory). Prepare to be dazzled by the spectral theory of automorphic forms.
