On the field generated by the periods of a Drinfeld module

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.