Skip to main content
MathOverflow

Return to Question

edited tags
Link
Andrés E. Caicedo
Andrés E. Caicedo
  • 32.5k
  • 5
  • 133
  • 240
formatting fixed
Source Link
edit approved Jul 8, 2013 at 22:00
András Bátkai
edit approved Jul 8, 2013 at 22:00
András Bátkai
  • 4.7k
  • 6
  • 31
  • 54

P(x,y,z)$P(x,y,z)$ is a polynomial function on an algebraic surface S$S$ in F_{q}^{3}$F_{q}^{3}$. Suppose that the derivative of P$P$ along any tangent vector of S$S$ is zero. Can we say that P$P$ is constant on S$S$?

Here q$q$ is a prime, and we assume the degrees of P$P$ and S$S$ are significantly smaller than q$q$.

P(x,y,z) is a polynomial function on an algebraic surface S in F_{q}^{3}. the derivative of P along any tangent vector of S is zero. Can we say that P is constant on S?

Here q is a prime, and we assume the degrees of P and S are significantly smaller than q.

$P(x,y,z)$ is a polynomial function on an algebraic surface $S$ in $F_{q}^{3}$. Suppose that the derivative of $P$ along any tangent vector of $S$ is zero. Can we say that $P$ is constant on $S$?

Here $q$ is a prime, and we assume the degrees of $P$ and $S$ are significantly smaller than $q$.

Source Link
Ben
Ben
  • 79
  • 1
  • 4

Calculus over finite fields

P(x,y,z) is a polynomial function on an algebraic surface S in F_{q}^{3}. the derivative of P along any tangent vector of S is zero. Can we say that P is constant on S?

Here q is a prime, and we assume the degrees of P and S are significantly smaller than q.