Explicit formulas for the exponential and logarithm of the Carlitz–Tate twist, and applications

Hasegawa, Takehiro

Journal de théorie des nombres de Bordeaux, Tome 36 (2024) no. 1, pp. 251-291

We present explicit formulas for the exponential and logarithm of the $n$th 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].

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].

Classification : 11G09, 11J91
Keywords: Carlitz–Tate twist, Anderson–Thakur exponential, Anderson–Thakur logarithm, Thakur hypergeometric function, log-type hypergeometric function

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