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math.NT2023
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…
math.NT2023
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…