TY - JOUR
T1 - Algebraic independence properties of the fredholm series
AU - Loxton, J. H.
AU - Van Der Poorten, A. J.
PY - 1978
Y1 - 1978
N2 - We consider algebraic independence properties of series such as [Formula Omitted] We show that the functions fr(z) are algebraically independent over the rational functions. Further, if αrs, (r = 2, 3, 4, …; s = 1, 2, 3, …) are algebraic numbers with [Formula Omitted], we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr-(αrs) over the rationals.
AB - We consider algebraic independence properties of series such as [Formula Omitted] We show that the functions fr(z) are algebraically independent over the rational functions. Further, if αrs, (r = 2, 3, 4, …; s = 1, 2, 3, …) are algebraic numbers with [Formula Omitted], we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr-(αrs) over the rationals.
UR - http://www.scopus.com/inward/record.url?scp=0010099828&partnerID=8YFLogxK
U2 - 10.1017/S1446788700011472
DO - 10.1017/S1446788700011472
M3 - Article
AN - SCOPUS:0010099828
SN - 1446-7887
VL - 26
SP - 31
EP - 45
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 1
ER -