A bound for rational Thurston–Bennequin invariants

In this paper, we introduce a rational τ invariant for rationally null-homologous knots in contact 3-manifolds with nontrivial Ozsváth–Szabó contact invariants. Such an invariant is an upper bound for the sum of rational Thurston–Bennequin invariant and the rational rotation number of the Legendrian representatives of the knot. In the special case of Floer simple knots in L-spaces, we can compute the rational τ invariants by correction terms.