Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-02T21:43:53.254Z Has data issue: false hasContentIssue false
  • English
  • Français

On approximation measures of q-logarithms

Published online by Cambridge University Press:  17 April 2009

Tapani Matala-Aho  and
Keijo Väänänen
Tapani Matala-Aho
Affiliation:
Department of Mathematical Sciences, University of Oulu, Linnanmaa 90570 Oulu, Finland e-mail: [email protected], [email protected]
Keijo Väänänen
Affiliation:
Department of Mathematical Sciences, University of Oulu, Linnanmaa 90570 Oulu, Finland e-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using Padé approximations of the q-logarithmic series we obtain new approximation measures for values of q-logarithms and for the series , k = 1, 2, …, where (un) is a recurrence sequence, satisfying

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 15 - 31
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]André-Jeannin, R., ‘Irrationalité de la somme des inverses de certaines suites récurrentes’, C.R. Acad. Sci. Paris, Sér. I Math. 308 (1989), 539–541.Google Scholar
[2]Andrews, G.E., The theory of partitions (Addison-Wesley, Reading MA, London, Amsterdam, 1976).Google Scholar
[3]Borwein, P.B., ‘On the irrationality of ∑(1/(qn + r))’ J. Number Theory 37 (1991), 253–259.CrossRefGoogle Scholar
[4]Borwein, P.B., ‘On the irrationality of certain series’, Math. Proc. Cambridge Philos. Soc. 112 (1992), 141–146.CrossRefGoogle Scholar
[5]Bundschuh, P. and Väänänen, K., ‘Arithmetical investigations of a certain infinite product’, Compositio Math. 91 (1994), 175–199.Google Scholar
[6]Duverney, D., ‘A propos de la série ’, J- Théor. Nombres Bordeaux 8 (1996), 173–181.CrossRefGoogle Scholar
[7]Duverney, D., Nishioka, K., Nishioka, K. and Shiokawa, I., ‘Transcendence of Jacobi's theta series and related results’ (to appear).Google Scholar
[8]Gel'fond, A.O., ‘Functions which take on integral values’, Mat. Zametki 1 (1967), 509–513; English translation, Math. Notes 1, 337–340.Google Scholar
[9]Matala-Aho, T., ‘Remarks on the arithmetic properties of certain hypergeometric series of Gauss and Heine’, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. 219 (1991), 1–112.Google Scholar
[10]Matala-Aho, T., ‘On Diophantine approximations of the Rogers-Ramanujan continued fraction’, J. Number Theory 45 (1993), 215–227.CrossRefGoogle Scholar
[11]Popov, A.Yu., ‘Arithmetical properties of the values of some infinite products’, (Russian), in Diophantine approximation 2, (Moskov Gos. Univ., Moscow, 1986), pp. 63–78.Google Scholar
[12]Stihl, T., ‘Arithmetische Eigenschaften spezieller Heinescher Reihen’, Math. Ann. 268 (1984), 21–41.CrossRefGoogle Scholar
[13]Väänänen, K., ‘On the approximation of certain infinite products’, Math. Scand. 73 (1993), 197–208.CrossRefGoogle Scholar