Stanley Yao Xiao

collaborators

3 papers

math.NT2024

Exponential sums over singular binary quartic forms and applications

Yasuhiro Ishitsuka, Takashi Taniguchi, Frank Thorne +1

We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in commo…

math.NT2023

Sextic polynomials in two variables do not represent all non-negative integers

Stanley Yao Xiao

In this paper we prove that for all degree $6$ polynomials with rational coefficients that $F (Z^{2}) \neq = Z_{\geq 0}$ . The answers a question of B. Poonen and J. S.…

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 $F \in Q [x, y]$ of degree $4$ such that $F (Z^{2}) = Z_{\geq 0}$ . In particular, this answers a question by…