On Toric Orbits in the Affine Sieve
On Toric Orbits in the Affine Sieve
We give a detailed analysis of a probabilistic heuristic model for the failure of "saturation" in instances of the Affine Sieve having toral Zariski closure. Based on this model, we formulate precise conjectures on several classical problems of arithmetic interest and test these against empirical data.