Publishing my work

Hello,

I am working on a math. paper (number theory) that I'd like to publish.
I never published any scientific papers before. I am doing this as an
amateur mathematician.

How do I go about it? I know there's arxiv.org where I can submit it.
Who is reviewing them? Are there any other sites/places I can submit my
paper for a review?

P.S. I live close to Princeton, NJ; but the folks at PU are difficult
to reach.

Thank you for your advice.

.

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