Make your work available (By Terence Tao)
We must get beyond textbooks, go out into the bypaths… and tell the world the glories of our journey. (John Hope Franklin)
With the advent of the internet and world-wide web, and in particular with preprint servers such as the arXiv, there is really no excuse not to make your preprints (or other publication-quality writing) available online, so that anyone who is interested in your work can easily find it. (Most journals now also have online availability, but given that the gap between preprint release and publication is measured in years, it still makes sense to have the preprint online too.)
In particular, your work will show up in search engine queries in your topic (I have come across many an interesting paper this way). This will help spread awareness of you and your work among your colleagues, and hopefully lead to future collaborations, or other people building upon (and citing) your papers.
One might be worried that by making your work available, you are inviting too much “competition” into your area, but if the area you work in is of that much interest to others, the competition will come anyway, and this way you will at least have priority (note that submissions to servers such as the arXiv have reliable timestamps) and be acknowledged in citations. Of course, one should still ensure that your preprints are written to publication-quality standard if at all possible, although this is not as important as it is with published papers since it is relatively easy to replace preprints with updated versions. [If you don’t have a preprint of your work yet, or only have a non-publication-quality draft, then it is often better to hold off on any announcement until you have something more concrete to show to other mathematicians.]
As to whether you should email your preprints to other experts in the field, I would only do this if the preprint is unquestionably of direct interest to that person (e.g. it solves a conjecture that they formulated). Otherwise there is the awkward possibility that the person you send the preprint to is too busy (or no longer interested in the topic) to read your work in detail, or that you might accidentally be perceived as being pushy, egotistic, or arrogant. (Also, to save yourself any embarrassment, it is a good idea to wait until your preprint is already at publication-level quality, and checked for errors, before sending it to other experts.)
In most cases it suffices to just make your work on-line; awareness of your work will spread by itself via several channels (e.g. the refereeing process, conferences, word-of-mouth, or preprint mailing lists) and there is usually little additional gain in trying to actively push the paper. But it is not a bad idea to have some place on your web page (or blog) in which you can make some comments (or “sales pitches”) on your own papers.
For similar reasons, I also recommend putting your professional information (cv, publication list, research interests, etc.) on your own web page, and keep it reasonably current (updating it at least once a year); this will allow others who are interested (or potentially interested) in your work to find out about you, without having to bother you directly.