Abstract

For any rank $2$ Drinfeld module $\rho$ defined over an algebraic function field, we consider its period matrix $P_{\rho}$, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field ${\Bbb F}_q$ is odd and that $\rho$ does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of $P_{\rho}$ over ${\Bbb F}_q(\theta)$ is $4$. As a consequence, we show also the algebraic independence of Drinfeld logarithms of algebraic functions which are linearly independent over ${\Bbb F}_q(\theta)$.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 359-391
Launched on MUSE
2011-03-24
Open Access
No
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