A few remarks on \(\zeta (3)\). (English. Russian original) Zbl 0888.11028

Math. Notes 59, No. 6, 625-636 (1996); translation from Mat. Zametki 59, No. 6, 865-880 (1996).
This is an exciting paper packed with wonderful formulas, valuable analysis, and useful explanations, which will surely interest the many ‘fans’ of Apéry’s astonishing proof in 1978 of the irrationality of \(\zeta(3)\) (see the reviewer’s ‘A proof that Euler missed …’ [A. J. van der Poorten, Math. Intell. 1, 195-203 (1979; Zbl 0409.10028)]. Specifically, the author analyses and applies ideas of L. A. Gutnik [Acta Arith. 42, 255-264 (1983; Zbl 0521.10028)] to produce a new view on Apéry’s proof. These notions give rise to the author’s extensive exploration of recurrence relations satisfied by a class of Meyer \(G\)-functions and lead to new continued fraction representations of \(\zeta(3)\). This paper gives one a fine response to provide to those writing to ask “what has happened to \(\zeta(3)\) since 1979?”.


11J72 Irrationality; linear independence over a field
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11J70 Continued fractions and generalizations
Full Text: DOI


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