Synaptic just gives me version 1.7.1, but I want version 1.7.3 without the need to download and build from sources.
Debian and Ubuntu often do no track the absolutely latest minor revision of a package that is actively developed unless there are significant feature fixes or security updates (and even in the even of such changes they will often backport the update for the significant change to the revision they do carry rather than picking up a whole new revision. This is particularly true of Debian/Stable and Ubuntu/Released in general and Debian/Testing and Ubuntu/Next close to release time (when they are in a "feature freeze" state).
To get a later version you have a few options:
Ubuntu/Natty currently carries 220.127.116.11-2 (which probably means "18.104.22.168 with at least two back-ported updates from later revisions"), the same as Debian/Queeze.
You could also try the version from Debian/Sid (though this is currently the same version) but this is not recommended. "Unstable" is given that name for a reason - packages may be broken at any given time as it exists specifically to find significant breakages before packages are promoted to Testing.
After having added following line
A way likely to work would be downloading from upstream and running the usual
inside the unpacked source directory.
Since in your edit you now explicitly write that you do not want to build from source and want 1.7.3 tagged on 2010/10/21 things look differently.
Ubuntu's git package seems to come directly from Debian's and Debian just migrated 22.214.171.124-2 to TESTING a week ago. You might have some luck with asking for a version bump in the Debian bug tracker, and could directly use that package in Ubuntu then.