Linear independence of values of $ E$-functions

Autor:	Yu. V. Nesterenko, A B Shidlovskii
Rok vydání:	1996
Předmět:	Discrete mathematics Algebraic cycle Algebra and Number Theory Function field of an algebraic variety Algebraic surface Real algebraic geometry Algebraic extension Algebraic function Algebraic independence Addition theorem Mathematics
Zdroj:	Sbornik: Mathematics. 187:1197-1211
ISSN:	1468-4802 1064-5616
Popis:	We prove a general theorem that establishes a relation between linear and algebraic independence of values at algebraic points of E-functions and properties of the ideal formed by all algebraic equations relating these functions over the field of rational functions. Using this theorem we prove sufficient conditions for linear independence of values of E-functions as well as for algebraic independence of values of subjects of them. The main result is an assertion stating that at all algebraic points, except finitely many, the values of E-functions are linearly independent over the field of all algebraic numbers if the corresponding functions are linearly independent over the field of rational functions. The theorem is applied to concrete E-functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::940e7c076ed6dc9ad8081a2232dcba90 https://doi.org/10.1070/sm1996v187n08abeh000152 Zobrazit plný text záznamu