Nous présentons des formules explicites pour l’exponentielle et le logarithme de la puissance tensorielle -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 sur les corps de fonctions définies dans notre article précédent [17].
We present explicit formulas for the exponential and logarithm of the th tensor power of the Carlitz module, introduced by Anderson and Thakur in 1990. We use these to prove transcendence results of the -type hypergeometric functions for function fields defined in our previous paper [17].
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Mots clés : Carlitz–Tate twist, Anderson–Thakur exponential, Anderson–Thakur logarithm, Thakur hypergeometric function, log-type hypergeometric function
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@article{JTNB_2024__36_1_251_0, author = {Takehiro Hasegawa}, title = {Explicit formulas for the exponential and logarithm of the {Carlitz{\textendash}Tate} twist, and applications}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {251--291}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {36}, number = {1}, year = {2024}, doi = {10.5802/jtnb.1278}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1278/} }
TY - JOUR AU - Takehiro Hasegawa TI - Explicit formulas for the exponential and logarithm of the Carlitz–Tate twist, and applications JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 251 EP - 291 VL - 36 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1278/ DO - 10.5802/jtnb.1278 LA - en ID - JTNB_2024__36_1_251_0 ER -
%0 Journal Article %A Takehiro Hasegawa %T Explicit formulas for the exponential and logarithm of the Carlitz–Tate twist, and applications %J Journal de théorie des nombres de Bordeaux %D 2024 %P 251-291 %V 36 %N 1 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1278/ %R 10.5802/jtnb.1278 %G en %F JTNB_2024__36_1_251_0
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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