4 papers
Covariants and simultaneous diagonalization of pairs of ternary quadratic forms, and binary quartic forms
Stanley Yao Xiao
In this paper we prove a correspondence between a canonical degree six covariant of binary quartic forms and a cubic covariant of a pair of ternary quadratic forms …
Hilbert's tenth problem for systems of diagonal quadratic forms, and Büchi's problem
Stanley Yao Xiao
In this paper we complete Büchi's proof that there is no decision algorithm for the solubility in integers of arbitrary systems of diagonal quadratic form equations, by proving the…
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…
Sextic polynomials in two variables do not represent all non-negative integers
Stanley Yao Xiao
In this paper we prove that for all degree polynomials with rational coefficients that . The answers a question of B. Poonen and J. S.…