A generalisation of Turán's main theorems to binomials and logarithms

A. J. Van Der Poorten*

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The Main Theorems of P. Turán's book Eine neue Methode in der Analysis und deren Anwendungen concern only sums of powers but are easily generalised to exponential sums with polynomial coefficients. It does not appear to have been observed however, that similar such theorems with analogous implication as to value distribution and arithmetical behaviour can be formulated for a wider class of functions. We prove a result for functions of the form [formula omitted] subsuming identities which Mahler has shown to contain transcendence results on the exponential and logarithmic functions and diophantine results of the Thue-Siegel-Roth type.

Original languageEnglish
Pages (from-to)183-195
Number of pages13
JournalBulletin of the Australian Mathematical Society
Volume2
Issue number2
DOIs
Publication statusPublished - 1970

Fingerprint Dive into the research topics of 'A generalisation of Turán's main theorems to binomials and logarithms'. Together they form a unique fingerprint.

  • Cite this