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Dans cet article, nous démontrons une inégalité liant la croissance d’un casoratien généralisé de séries entières -adique à la croissance du casoratien ordinaire de ces séries entières. Il en résulte que si le casoratien de fonctions entières -adiques est un polynôme non nul, alors toutes ces fonctions sont des polynômes. Comme application, nous montrons que si une équation aux différences linéaire d’ordre à coefficients dans a solutions méromorphes dans tout , linéairement indépendantes...
The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.
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