We give L^2-signature obstructions to embedding closed 3-manifolds with infinite cyclic first homology in closed 4-manifolds with infinite cyclic fundamental group preserving first homology. From the obstructions, we obtain lower bounds on the double slice genus of a knot, and give examples of algebraically doubly slice knots with vanishing Casson-Gordon invariants whose double slice genera are arbitrarily large. This is a joint work with Taehee Kim.