In his 2009 autobiography, “ Random Curves,” Neal I. Koblitz, a University of Washington mathematician who aided Mr. Vaughn and was one of two inventors of the technique, described its ...

We prove an asymptotic formula for the number of SL3 (ℤ)-equivalence classes of integral ternary cubic forms having bounded invariants. We use this result to show that the average size of the 3-Selmer ...

A very general surface of degree at least four in P3 contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in P3 of degree at least five ...