In Longisquama, it has long been accepted, that a frill of several
extraordinarily long (feather-like) (scale-like) plumes arose from the
dorsal sector of the vertebral series. About three years ago I published
that Longisquama, along with Sharovipteryx, Cosesaurus and other
Prolacertiforms were sister taxa to the Pterosauria. Recent work (as yet
unpublished) describing the posterior of Longisquama, the prepubis of
Sharovipterys, etc. confirms that association.
I wrote to a leading expert on pterosaur aerodynamics early on and asked
for his opinion on the subject - how would such a structure affect
flight, etc. Still waiting for an answer on that one. Since it was
totally unexpected and still paradigm-shaking, I don't mind that it
takes some time to arrive at a carefully considered answer. No doubt it
was a display structure. Sailfish may have an analogous structure and
they are among the fastest fish in the sea. I have not seen a pterosaur
dorsal frill that was anything less than completely erect.