3 citations · 8 across the 8 of their papers we have counts for
4 papers · 2 filters
Uniformity of fibres of period mappings and the -unit equation
Brett Nasserden, Stanley Yao Xiao
In this paper we give a refinement of the method introduced by Lawrence and Venkatesh and thereby showing that their proof of Mordell's conjecture is uniform up to a uniform bound…
On the -Pell equation
Erick Knight, Stanley Yao Xiao
Let , where is a primitive root of unity. In this paper we study the distribution of integers for which the norm equation $N_{K(\sqr…
The negative Pell equation
Erick Knight, Stanley Yao Xiao
By applying methods recently developed by A. Smith with regards to Goldfeld's conjecture, we show that the density of square-free integers in for which the negative Pe…
On monic abelian cubics
Stanley Yao Xiao
In this paper we prove the assertion that the number of monic cubic polynomials with integer coefficients and irreducible, Galois over $\mathbb…