Variations on the Arkhipov-Karačuba Type Counterexamples to Artin's Conjecture

Zhaobo Tom Han

It was conjectured by Emil Artin in the 1930's that every $d$-form $F(x_1,x_2,$\ldots$,x_n)$ over the $p$-adic field in more than $d^2$ variables has a solution that is not $(0,…