We will now move on to think of these same functions in a different way from the previous chapter. We will examine different limits in number theory, and how integrals and calculus are inextricably bound up with this sort of question.

If, after this chapter, you are interested in more of this kind of material, definitely check out¹Two other books with useful presentations are the terse one in [C.1.9] and the more intuitive, if shorter, one in [C.1.11]. Stopple's excellent [C.3.5], to which I am indebted for many of the ideas here, or the more challenging book [C.3.6] by Apostol.

Finally, note that some proficiency in calculus is helpful in understanding the results in this chapter, though a proper course is not necessarily a prerequisite.