On simultaneous diophantine approximations to ζ(2) and ζ(3)

Title: On simultaneous diophantine approximations to ζ(2) and ζ(3)
Creator: Dauguet, Simon; Zudilin, Wadim
Relation: Journal of Number Theory Vol. 145, p. 362-387
Publisher Link: http://dx.doi.org/10.1016/j.jnt.2014.06.007
Publisher: Academic Press
Resource Type: journal article
Date: 2014
Description: We present a hypergeometric construction of rational approximations to ζ(2) and ζ(3) which allows one to demonstrate simultaneously the irrationality of each of the zeta values, as well as to estimate from below certain linear forms in 1, ζ(2) and ζ(3) with rational coefficients. We then go further to formalize the arithmetic structure of these specific linear forms by introducing a new notion of (simultaneous) diophantine exponent. Finally, we study the properties of this newer concept and link it to the classical irrationality exponent and its generalizations given recently by S. Fischler.
Subject: irrationality; diophantine approximation; irrationality exponent; value of Riemann's zeta function; hypergeometric series; hypergoemetric integral; recurrence equation; algorithm of creative telescoping
Identifier: http://hdl.handle.net/1959.13/1298088
Identifier: uon:19583
Identifier: ISSN:0022-314X
Language: eng
Reviewed

		Thumbnail	File	Description	Size	Format