Abstract
Generalizing the results of Maurischat in [4], we show that the field \(K_{\infty }(\Lambda )\) of periods of a Drinfeld module \(\phi \) of rank r defined over \(K_{\infty } = \mathbb {F}_{q}((T^{-1}))\) may be arbitrarily large over \(K_{\infty }\). We also show that, in contrast, the residue class degree \(f( K_{\infty }(\Lambda ) | K_{\infty })\) remains bounded by a constant that depends only on r.
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References
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Gekeler, EU. On the field generated by the periods of a Drinfeld module. Arch. Math. 113, 581–591 (2019). https://doi.org/10.1007/s00013-019-01379-6
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DOI: https://doi.org/10.1007/s00013-019-01379-6