3 papers
math.NT2024
Integers expressible as the sum of two rational cubes
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We prove that a positive proportion of integers are expressible as the sum of two rational cubes, and a positive proportion are not so expressible, thus proving a conjecture of Dav…
math.NT2024
Quadrics in arithmetic statistics
Levent Alpöge
We (re)introduce the circle method into arithmetic statistics. More specifically, we combine the circle method with Bhargava's counting technique in order to give a general method…
math.NT2024
Conditional algorithmic Mordell
Levent Alpöge, Brian Lawrence
We specify a Turing machine with the following properties. 1. On input , with a number field and a smooth projective hyperbolic c…