Algebraic relations among periods and logarithms of rank 2 Drinfeld modules Academic Article uri icon

abstract

  • For any rank 2 Drinfeld module ρ defined over an algebraic function field, we consider its period matrix P ρ , which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field F q is odd and that ρ does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of P ρ over F q (θ) is 4. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over F q (θ). © 2011 by The Johns Hopkins University Press.

author list (cited authors)

  • Chang, C., & Papanikolas, M. A.

citation count

  • 7

publication date

  • January 2011