Suppose we have two observers A and B. A is in some inertial frame. B is undergoing uniform circular motion with some speed $v$ as observed by A. They each have a clock.
My concern is with what A sees when looking at B's clock and what B sees when looking at A's clock.
I expect A will see B's clock slowed down... according to A it will take $\gamma$ seconds for B's clock to tick 1 second. This is the standard time dilation formula. Is this right?
But how does one analyze how B sees A's clock using only special relativity?