The download over https on a Galaxy S3/4 just shows "in progress" for a while and then eventually fails.
I created a new site in IIS7 with 2 files: "pdf.pdf" and "index.html". I've set the bindings of the site to static.local.com for http and https(self signed cert) and my host file points static.local.com to 127.0.0.1.
Contents of index.html
<html>
<head></head>
<body>
<a href="https://static.local.com/pdf.pdf" target="_blank">link</a>
<a href="http://static.local.com/pdf.pdf" target="_blank">link</a>
</body>
</html>
Only the http link works on the Galaxy S3/4. Also this scenario has been tested with a valid SSL cert. I see this issue posted all over the internet of people having issues downloading pdfs over https, but was hoping someone had a workaround that doesn't involve using another browser, download works with Opera-mini.