The Riemann zeta-function, which encodes information about the integers and the prime numbers, has been studied extensively. Its values at 2,4,... are well-known, but much less is known about its values at 3,5,... . This difference can be explained to an extent by the different behaviour of certain groups (algebraic K-groups) of the rationals. In this talk, we discuss some basic examples of such K-groups, and some links between them and arithmetic.