In algebraic number theory a number of situations arise in which knowing how a prime splits in a field depending on the prime can be important. I will give a number of motivating examples and try my best to explain some of the analytic techniques involved – I’m just learning them myself. I’ll also explain that while the primes with one splitting behavior might have density 1/3 and the rest density 2/3, it is extremely unlikely Chebotarev’s theorem is playing a role.

Part 2 of 2.