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- W2950093395 abstract "Let $K$ be a number field, $UX$ be a smooth projective curve over it and $D$ be a reduced divisor on $UX$. Let $(E,nabla)$ be a fibre bundle with connection having meromorphic poles on $D$. Let $p_1,...,p_sinUX(K)$ and $X:=UXsetminus{D,p_1,..., p_s}$ (the $p_j$'s may be in the support of $D$). Using tools from Nevanlinna theory and formal geometry, we give the definition of $E$--section of type $alpha$ of the vector bundle $E$ with respect to the points $p_j$; this is the natural generalization of the notion of $E$ function defined in Siegel Shidlowski theory. We prove that the value of a $E$--section of type $alpha$ in an algebraic point different from the $p_j$'s has maximal transcendence degree. Siegel Shidlowski theorem is a special case of the theorem proved. We give an application to isomonodromic connections." @default.
- W2950093395 created "2019-06-27" @default.
- W2950093395 creator A5047167459 @default.
- W2950093395 date "2009-10-07" @default.
- W2950093395 modified "2023-09-27" @default.
- W2950093395 title "Horizontal sections of connections on curves and transcendence" @default.
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