On the generalized Carlitz module

Federico Pellarin (1)

1 ICJ - Institut Camille Jordan

The aim of this note is to gather formal similarities between two apparently different functions; {\em Euler's function} $\Gamma$ and {\em Anderson-Thakur function} $\omega$. We discuss these similarities in the framework of the {\em generalized Carlitz's module}, a common structure which can be helpful in framing the theories of both functions. We further analyze several noticeable differences while investigating the {\em exponential functions} associated to these structures.

Mots clés: Carlitz module; gamma function; Akhiezer-Baker functions

Domaines: Théorie des nombres [math.NT]

Federico Pellarin. On the generalized Carlitz module. Journal of Number Theory, 2013, 133 (5), pp.1663-1692. ⟨10.1016/j.jnt.2012.10.009⟩. ⟨hal-00739761v2⟩