Do Mathematics Grad schools in the US expect a research paper from a Masters Student for admission into a PhD Program?
As mentioned in the comments, no.  In the US, there are typically 2 master's tracks one can take: a thesis option (with some coursework) or a non-thesis option (more coursework + exams).  Most students I know who do master's degrees in the US (many of whome go on to PhD programs) do the non-thesis option.  In fact, many undergrads do a non-thesis masters (or something like Cambridge's Part III) to help them get into good PhD programs.  So in the US, in contrast to some countries like Japan, it is not expected.