Explicit formulas for the exponential and logarithm of the Carlitz–Tate twist, and applications
Takehiro Hasegawa1
1 Shiga University, Otsu, Shiga 520-0862 Japan
Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 1, pp. 251-291.

Nous présentons des formules explicites pour l’exponentielle et le logarithme de la puissance tensorielle n-ième du module de Carlitz, introduit par Anderson et Thakur en 1990. Nous les utilisons pour prouver des résultats de transcendance pour les fonctions hypergéométriques de type log sur les corps de fonctions définies dans notre article précédent [17].

We present explicit formulas for the exponential and logarithm of the nth tensor power of the Carlitz module, introduced by Anderson and Thakur in 1990. We use these to prove transcendence results of the log-type hypergeometric functions for function fields defined in our previous paper [17].

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DOI : 10.5802/jtnb.1278
Classification : 11G09, 11J91
Mots clés : Carlitz–Tate twist, Anderson–Thakur exponential, Anderson–Thakur logarithm, Thakur hypergeometric function, log-type hypergeometric function
Takehiro Hasegawa 1

1 Shiga University, Otsu, Shiga 520-0862 Japan
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Takehiro Hasegawa. Explicit formulas for the exponential and logarithm of the Carlitz–Tate twist, and applications. Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 1, pp. 251-291. doi : 10.5802/jtnb.1278. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1278/

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