题目：Some Arithmetic Functions and Chebotarev Densities
For the Möbius function , it is well-known that the prime number theorem is equivalent to . In 1977, Alladi showed a formula on a restricted sum of . In 2017, Dawsey generalized Alladi's result to the setting of Chebotarev densities for finite Galois extensions of Q. In this talk, we will introduce the analogues of their formulas with respect to the Liouville function and the Ramanujan sum, which are closely related to the Möbius function. All are welcome.