Frobenius difference equations and algebraic independence of zeta values in positive equal characteristic Academic Article uri icon


  • By analogy with the Riemann zeta function at positive integers, for each finite field F pr with fixed characteristic p, we consider Carlitz zeta values ζ r (n)at positive integers n. Our theorem asserts that among the zeta values in the set U ∞r=1 {ζ r (1), ζ r (2), ζ r (3),...}, all the algebraic relations are those relations within each individual family {ζ r (1), ζ r (2), ζ r (3),...}. These are the algebraic relations coming from the Euler-Carlitz and Frobenius relations. To prove this, a motivic method for extracting algebraic independence results from systems of Frobenius difference equations is developed.

author list (cited authors)

  • Chang, C., Papanikolas, M., & Yu, J.

citation count

  • 1

publication date

  • August 2011