Polynomials meeting Ax’s bound

Abstract

Let $f\in\Bbb F_q[X_1,\dots,X_n]$ with $\mathop{\rm deg} f=d \gt 0$ and let $Z(f)=\{(x_1,\dots,x_n)\in \Bbb F_q^n: f(x_1,\dots,x_n)=0\}$. Ax’s theorem states that $|Z(f)|\equiv 0\pmod {q^{\lceil n/d\rceil-1}}$, that is, $\nu_p(|Z(f)|)\ge m(\lceil n/d\rcei

Locations

• Acta Arithmetica - View
• arXiv (Cornell University) - View - PDF