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Arithmetical Results on Certain Multivariate Power Series
Author(s) -
Bundschuh P.,
Zhou P.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305018242
Subject(s) - arithmetic function , mathematics , radius of convergence , series (stratigraphy) , power series , sequence (biology) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , paleontology , genetics , biology
Power series∑ n = 0 ∞ f ( n ) x nwith non‐zero convergence radius R ( f ) are considered, and the arithmetical nature (that is, irrationality, or even transcendence) of the corresponding multivariate series∑ i 1 , … , i m = 0 ∞ f ( i 1 + + i m ) x 1 i 1· … · x m i mis studied if x 1 , …, x m and the sequence ( f ( n )) satisfy appropriate arithmetical conditions. It follows that such arithmetical results can be written down easily if linear independence results on the function F ( x ), defined in | x | < R ( f ) by the original one‐dimensional power series, and possibly its derivatives at the points x μ are known. Some typical applications are explicitly stated. 2000 Mathematics Subject Classification 11J72.