On the value of Dedekind sums and eta-invariants for 3-dimensional lens spaces (Q1097910)

If [x] is the greatest integer in x and p,q are relatively prime positive integers, the sum \(\sum^{q-1}_{k=1}[kp/q]\) 2 is essentially a Dedekind sum. The author shows that this sum can be expressed as a polynomial in p,q and a sequence of integers \([q_{i-1}/q_ i]\) defined recursively in terms of p and q. The sum is also related to the eta- invariant \(\eta\) (p,q) for the 3-dimensional lens space L(p;q).