Some arithmetic properties of the CWL invariant

To derive information about rational homology 3-spheres via the Casson-Walker-Lescop (CWL) invariant λ, this paper focuses on the fractional part of the invariant, completes the determination of the fractional parts of λ for homology lens spaces, shows that the fractional part is an invariant of the linking forms mod Z for homology lens spaces and gives a complete set of invariants derived from λ to classify the linking forms mod Z.