The aim of this note is to gather formal similarities between two apparently different functions; Euler’s function Γ and Anderson-Thakur function ω. We discuss these similarities in the framework of the 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 exponential functions associated to these structures.
On the generalized Carlitz module / Pellarin, Federico. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 133:5(2013), pp. 1663-1692. [10.1016/j.jnt.2012.10.009]
On the generalized Carlitz module
Federico Pellarin
2013
Abstract
The aim of this note is to gather formal similarities between two apparently different functions; Euler’s function Γ and Anderson-Thakur function ω. We discuss these similarities in the framework of the 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 exponential functions associated to these structures.File allegati a questo prodotto
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