AN APPLICATION OF NESTERENKO'S DIMENSION ESTIMATE TO p-ADIC q-SERIES-Reference-Cited by-同舟云学术

AN APPLICATION OF NESTERENKO'S DIMENSION ESTIMATE TO p-ADIC q-SERIES

Published:2011-03 Issue:02 Volume:07 Page:431-447
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BUNDSCHUH PETER¹,VÄÄNÄNEN KEIJO²

Affiliation:

1. Universität zu Köln, Mathematisches Institut, Weyertal 86-90, 50931 Köln, Germany

2. University of Oulu, Department of Mathematical Sciences, P.O. Box 3000, 90014 Oulu, Finland

Abstract

Very recently, Nesterenko proved a p-adic analogue of his famous dimension estimate from 1985. The main aim of our present paper is to use this criterion to obtain lower bounds for the dimension of ℚ-vector spaces spanned by the values at certain rational points of p-adic solutions of a class of linear q-difference equations. For the application of Nesterenko's new estimate, we first need a p-adic analogue of Töpfer's results on entire solutions of such functional equations, and secondly, very precise evaluations of certain p-adic Schnirelman integrals.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042111004071

Reference5 articles.

1. Transcendental Numbers in the P-Adic Domain

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3. ARITHMETICAL RESULTS ON CERTAIN q-SERIES, II

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5. ARITHMETICAL PROPERTIES OF FUNCTIONS SATISFYING q-DLFFERENCE EQUATIONS

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