To answer your specific questions...
Does nutrient availability limit emergence depth?
Yes, the size of the nutrient store in the seed does impose a theoretical limit on the maximum depth at which seed germination and emergence can take place.
What is the best depth for a given species?
The specific depth which gives best germination for any given species is very unlikely to be the maximum depth at which seeds of that species can germinate. This is because other factors also impose limits on germination depth.
Probably the most important other factor is light - most seeds require the perception of red light in order to trigger germination. For most species then, you are unlikely to find seeds germinating and successfully emerging from depths greater than the penetrance of light.
Another important factor in some latitudes is temperature - many seeds (from 26 families) use dormancy as a way of preventing germination in the wrong seasonal conditions. In species where temperature serves as a cue to alleviate dormancy, there will be a maximum depth at which a given seed can detect the temperature fluctuations at the surface. Beyond a certain depth, surface temperature changes will not perceptibly affect local temperature.
If you ever need to find out the best depth of germination for a given species, many can be found on google, or failing that it is trivial to perform a simple experiment.
Is there a mathematical relationship?
There is a general mathematical relationship, an allometric relationship (i.e. relating size to another trait), between seed size and maximum depth of emergence, described by Bond et al. (1999):
dmax = maximum depth of emergence
w = seed weight
c = a constant which varies with phylogeny and environmental conditions.
Many species however will not submit to this equation. For example some large-seeded species (incl. coconut, coco-de-mer, avocado), have large seeds because they may need to enable long-distance growth along the ground in order to locate optimum growth conditions. Seeds of these species will therefore not conform to the depth-size relationship above.