Integer valued functions and Carlitz module
Let be the Carlitz module, let and let be the set . in this article, we prove that if an entire function has a quadratic type and takes integer values over , then it is a polynomial. The bound is optimal. This is an analog for the finite characteristic case of Pólya-Gel’fond’s theorem.
Soient le module de Carlitz, un polynôme de et l’ensemble . Nous montrons qu’une fonction entière de type quadratique qui prend des valeurs entières sur , est polynomiale. De plus, la borne est optimale. Ceci est un analogue en caractéristique finie du théorème de Gel’fond-Pólya.
@article{JTNB_2010__22_2_271_0, author = {David Adam}, title = {Fonctions \`a valeurs enti\`eres et module de {Carlitz}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {271--286}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {2}, year = {2010}, doi = {10.5802/jtnb.715}, mrnumber = {2769062}, zbl = {1235.13015}, language = {fr}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.715/} }
TY - JOUR AU - David Adam TI - Fonctions à valeurs entières et module de Carlitz JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 271 EP - 286 VL - 22 IS - 2 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.715/ DO - 10.5802/jtnb.715 LA - fr ID - JTNB_2010__22_2_271_0 ER -
%0 Journal Article %A David Adam %T Fonctions à valeurs entières et module de Carlitz %J Journal de théorie des nombres de Bordeaux %D 2010 %P 271-286 %V 22 %N 2 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.715/ %R 10.5802/jtnb.715 %G fr %F JTNB_2010__22_2_271_0
David Adam. Fonctions à valeurs entières et module de Carlitz. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 271-286. doi : 10.5802/jtnb.715. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.715/
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