In number theory, various "prime geodesic theorems" have been proved which are very similar in spirit to the prime number theorem. To be specific, we let π("x") denote the number of closed geodesics whose norm (a function related to length) is less than or equal to "x"; then π("x") ∼ "x"/ln("x"). This result is usually credited to Atle Selberg. In his 1970 Ph.D. thesis, Grigory Margulis proved a similar result for surfaces of variable negative curvature, while in his 1980 Ph.D. thesis, Peter Sarnak proved an analogue of Chebotarev's density theorem.