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Archiv der Mathematik

, Volume 113, Issue 3, pp 247–254 | Cite as

On field extensions given by periods of Drinfeld modules

  • Andreas MaurischatEmail author
Article

Abstract

In this short note, we answer a question raised by M. Papikian on a universal upper bound for the degree of the extension of \(K_\infty \) given by adjoining the periods of a Drinfeld module of rank 2. We show that contrary to the rank 1 case such a universal upper bound does not exist, and the proof generalies to higher rank. Moreover, we give an upper and lower bound for the extension degree depending on the valuations of the defining coefficients of the Drinfeld module. In particular, the lower bound shows the non-existence of a universal upper bound.

Keywords

Drinfeld modules Periods Field extensions Newton polygons 

Mathematics Subject Classification

11G09 

Notes

References

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.RWTH Aachen UniversityAachenGermany

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