The average elliptic curve has few integral points
Add to your list(s)
Download to your calendar using vCal
 Levent Alpoge (Cambridge)
 Tuesday 26 May 2015, 16:1517:15
 MR13.
If you have a question about this talk, please contact Jack Thorne.
It is a theorem of Siegel that the Weierstrass model y^2 = x^3 + A x + B of an elliptic curve has finitely many integral points. A “random” such curve should have no points at all. I will show that the
average number of integral points on such curves (ordered by height)
is bounded—in fact, by 66. The methods combine a Mumfordtype gap
principle, LP bounds in sphere packing, and results in Diophantine approximation. The same result also holds (though I have not computed
an explicit constant) for the families y^2 = x^3 + A x , y^2 = x^3 + B ,
and y^2 = x^3  n^2 x .
This talk is part of the Number Theory Seminar series.
This talk is included in these lists:
Note that exdirectory lists are not shown.
