Number Theory

    

Transcendence of Deformations of Polylogarithm Functions in Non-Zero Characteristic

Authors: David Adam

Let p be a prime number. In 2005, with the aim of reproving by Wade's method the transcendence for n ∈ Zp N of Γ∞(n), where Γ∞ is the Carlitz-Goss factorial, Yao introduces an uncountable class of deformations of Kochubei polylogarithm functions of which he shows the transcendence of their values u200bu200bin 1 (which is sufficient for his objective) and more generallyin 1/T^k (k ∈ N∗). In this present article, we answer Yao's question to extend this result into a non-zero algebraic. We prove this fact not only in the context of infinite place but also in that of finite places. We show an analogous result for the deformations of the polylogarithm function of Carlitz.

Comments: 15 Pages. In French

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Submission history

[v1] 2024-07-03 18:58:58

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