I need to solve the following integral $$\int\limits_{\left| {s - a} \right| = \delta } {\frac{{{\mathop{\rm sgn}} (is)}}{{{e^{2\pi irs}}}}ds}$$
Where the contour is the semicircle in the upper half plane oriented clockwise.
I attempted the solution using Sato's hyperfunctions, which really only made things unnecessarily difficult. I'm sure there is a simple solution, I'm just not accustomed to contour integration with generalized functions in the integrand. Can anyone help me out?
