Un théorème de transcendance en caractéristique finie
Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, p. 57-82

Let p be a prime number, and q=p r , with r0. Let k=𝔽 q (T), and k ¯ be its algebraic closure. We can associate to any Drinfeld module of rank 2, a modular invariant j, and also modular functions. We are interesting in one of them, denoted Δ ¯. In particular, we show that if |t|<q -1 q-1 then at least one of the two numbers j(t) and Δ ¯(t) is transcendental over k.

Soit p un nombre premier et q=p r , où r est non nul. On considère le corps k=𝔽 q (T), dont on note k ¯ une clôture algébrique. On peut associer à tout module de Drinfeld de rang 2, défini sur k ¯, un invariant modulaire j, ainsi que des fonctions modulaires. On s'intéresse à l'une d'entre elles, notée Δ ¯. On montre en particulier, que si |t|<q -1 q-1 alors l'un au moins des deux nombres j(t) et Δ ¯(t) est transcendant sur k.

@article{JTNB_2003__15_1_57_0,
     author = {Dion, Sophie},
     title = {Un th\'eor\`eme de transcendance en caract\'eristique finie},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     pages = {57-82},
     zbl = {1049.11080},
     mrnumber = {2019001},
     language = {fr},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_57_0}
}
Dion, Sophie. Un théorème de transcendance en caractéristique finie. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 57-82. http://www.numdam.org/item/JTNB_2003__15_1_57_0/

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