Algebraic relations among periods and logarithms of rank 2 Drinfeld modules

Abstract

For any rank 2 Drinfeld module rho defined over an algebraic function field, we consider its period matrix P, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of F_q is odd and rho is without complex multiplication. We show that the transcendence degree of the field generated by the entries of P over F_q(theta) is 4. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over F_q(theta).

25 pages

References in corpus (2)

• Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms
• Determination of the algebraic relations among special Gamma-values in positive characteristic

Cited by in corpus (2)

• Geometric Gamma values and zeta values in positive characteristic
• Algebraic independence of arithmetic gamma values and Carlitz zeta values