ecco le prove che ho fatto invano:

1)
header("Content-type: application/pdf");
header("Content-Disposition: attachment; filename=downloaded.pdf");

2)
$filename="prova.pdf";
header ("Content-Type: application/pdf");
header ("Content-Disposition: inline; filename=$filename");

3)
$filename="prova.pdf";
header ("Content-Type: application/vnd.pdf");
header ("Content-Disposition: inline; filename=$filename");