Algebraic independence properties of the fredholm series

J. H. Loxton; A. J. Van Der Poorten

doi:10.1017/S1446788700011472

Algebraic independence properties of the fredholm series

J. H. Loxton, A. J. Van Der Poorten

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	31-45
Number of pages	15
Journal	Journal of the Australian Mathematical Society
Volume	26
Issue number	1
DOIs	https://doi.org/10.1017/S1446788700011472
Publication status	Published - 1978
Externally published	Yes

Access to Document

10.1017/S1446788700011472

Cite this

@article{0f6a908e46244761aa9285b4442850cf,

title = "Algebraic independence properties of the fredholm series",

abstract = "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.",

author = "Loxton, \{J. H.\} and \{Van Der Poorten\}, \{A. J.\}",

year = "1978",

doi = "10.1017/S1446788700011472",

language = "English",

volume = "26",

pages = "31--45",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Cambridge University Press (CUP)",

number = "1",

}

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 - https://www.scopus.com/pages/publications/0010099828

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 -

Algebraic independence properties of the fredholm series

Abstract

Access to Document

Other files and links

Fingerprint

Cite this