21 citations · 38 across the 13 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
Note on a theorem of Professor X
Levent Alpöge
Between his arrival in Frankfurt in and and his proof of his famous finiteness theorem for integral points in , Siegel had no publications. He did, however, write a le…
Modularity and effective Mordell I
Levent Alpöge
We give an effective proof of Faltings' theorem for curves mapping to Hilbert modular stacks over odd-degree totally real fields. We do this by giving an effective proof of the Sha…
The second moment of the number of integral points on elliptic curves is bounded
Levent Alpöge, Wei Ho
Let be a number field and a finite set of places of containing all archimedean places. In this paper, we show that the second moment of the number of -integral point…
The average number of rational points on genus two curves is bounded
Levent Alpoge
We prove that, when genus two curves with a marked Weierstass point are ordered by height, the average number of rational points is bounded. The…
The average number of integral points on elliptic curves is bounded
Levent Alpoge
We prove that, when elliptic curves are ordered by height, the average number of integral points is bounded, and in fact is less than (and a…
Maass waveforms and low-lying zeros
Levent Alpoge, Nadine Amersi, Geoffrey Iyer +3
The Katz-Sarnak Density Conjecture states that the behavior of zeros of a family of -functions near the central point (as the conductors tend to zero) agrees with the behavior o…
Low-lying zeroes of Maass form -functions
Levent Alpoge, Steven J. Miller
The Katz-Sarnak density conjecture states that the scaling limits of the distributions of zeros of families of automorphic -functions agree with the scaling limits of eigenvalue…