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 $\varphi$ 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 $r$.

11 pages