2 papers
math.NT2025
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 …
math.NT2025
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 th…