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i'm studying the functional equation of riemann zeta function for Re(s)>1;

my book(complex analysis by T. Gamelin) use contour integral in the proof, where the contour is taken on the usual 3 curves (real axis and a small circle [tex]C\epsilon[/tex] around the origin). i'm not able to figure why the integral on the circle vanish as epsilon->0; the text report:

since [tex]e^{z -1}[/tex] has a simple zero at z=0, the integrand is bounded on the circle |z|=r by C [tex]\epsilon^{re(s)-2}[/tex]

wich is the estimate that the author use in this assertion?

i'm new to complex analysis and i want to say (if possible) what argument i've got to study

thanks

I.M.

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# Help for zeta functional equation

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