Algebraic relations among periods and logarithms of rank 2 Drinfeld modules

Details Algebraic relations among periods and logarithms of rank 2 Drinfeld modules Algebraic relations among periods and logarithms of rank 2 Drinfeld modules

2008-07-20

arxiv.org/abs/0807.3157v1

Amer. J. Math. 133 (2011), 359-391

Mathematics

Number Theory

25 pages

Scientific paper

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).

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