"Sign In To iTunes Store" messages for Apple IDs that aren't mine

"Sign In To iTunes Store" messages for Apple IDs that aren't mine

I just got a new iPhone, and every day or so I get a series of about 7 or 8 pop ups in a row to "Sign In to iTunes Store" for some spammy-looking email addresses/Apple IDs. The strange thing is I remember this happening when I got my last phone but I don't know how I got them to stop or if they stopped on their own. I've had this phone for about a month now and they're not going away.

Some of the Apple IDs that pop up:

****

...And others like that. Why is my phone thinking these Apple IDs are active on my phone somewhere? Do I have some rogue application that's registered in their name or something? Is there a way to even tell?