2
votes
1answer
59 views

Integration of complex function with respect to complex variable

I was given as homework to calculate the complex integral limit $$\lim_{T\rightarrow \infty} \frac {1}{2\pi i}\int_{c-iT}^{c+iT}\frac {x^s}{s^{k+1}}ds $$ where $c>0$ and $k\geq1$ is an integer. ...
5
votes
2answers
148 views

“Convergent” Integral in Davenport's Multiplicative Number Theory

I am currently learning analytic number theory using Davenport's Multiplicative Number Theory book, and at some point I believe something silly is happening. I have great faith that I am wrong AND ...