2 citations · 4 across the 6 of their papers we have counts for
10 papers · 1 filter
Quartic polynomials in two variables do not represent all non-negative integers
Stanley Yao Xiao, Shuntaro Yamagishi
In this paper, we prove that there does not exist of degree such that . In particular, this answers a question by…
Elliptic curves with a rational 2-torsion point ordered by conductor and the boundedness of average rank
Stanley Yao Xiao
In this paper we refine recent work due to A. Shankar, A. N. Shankar, and X. Wang on counting elliptic curves by conductor to the case of elliptic curves with a rational 2-torsion…
The density of rational points on with three stacky points
Brett Nasserden, Stanley Yao Xiao
In this paper we consider the density of rational points on the "stacky" curve which is with three half points, with res…
Density of power-free values of polynomials II
Kostadinka Lapkova, Stanley Yao Xiao
In this paper we prove that polynomials of degree , satisfying certain hypotheses, take on the expected density of…
A stratification result for an exponential sum modulo
Kostadinka Lapkova, Stanley Yao Xiao
In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials in the quotient ri…
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…