Abstract
Lete and π be the Carlitz-module analogues of their usual counterparts. We have proved in [4]-that these elements of\(\mathbb{F}_q ((1/T))\) are algebraically independent over\(\mathbb{F}_q (T)\) whenq≥3. We study here the remaining caseq=2 and prove among other things that 1,e, π are linearly independent over\(\mathbb{F}_2 (T)\).
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