On the field generated by the periods of a Drinfeld module
Abstract
Generalizing the results of Maurischat in \cite{Maurischatxx}, we show that the field $K_{\infty}(\Lambda)$ of periods of a Drinfeld module $\phi$ of rank $r$ defined over $K_{\infty} = \mathds{F}_{q}((T^{-1}))$ 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 $r$.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.11432
- arXiv:
- arXiv:1905.11432
- Bibcode:
- 2019arXiv190511432G
- Keywords:
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- Mathematics - Number Theory;
- 11G09
- E-Print:
- 11 pages