There is a thread in Deals [Sony Reader App for iPhone/iPad/iTouch
] and one in the Sony Forum [Cannot sign into Sony Reader app for iPad
] about the app. There were some problems at first with signing into the app with your adobe ID.
It took me a while to find it in the app store, as it is just called "Reader", and I kept searching for "Sony". The app has a green background with a white outline of an open book. It looks like it was developed by Bluefire.