Construction of Approximations to Zeta-Values

Nesterenko, Yuri V.

doi:10.1007/978-3-211-74280-8_16

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“…contains infinitely many irrational zeta constants, see [8]. Various advanced techniques for studying the zeta constants are surveyed in [28], and [37].…”

Section: Introductionmentioning

confidence: 99%

Irrationality of the Zeta Constants

Carella

2012

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A general technique for proving the irrationality of the zeta constants ζ(2n + 1), n ≥ 1, from the known irrationality of the beta constants L(2n + 1, χ) is developed in this note. The irrationality of the zeta constants ζ(2n), n ≥ 1, and ζ(3) are well known, but the irrationality results for the zeta constants ζ(2n + 1), n ≥ 2, are new, and seem to show that these are irrational numbers. By symmetry, the irrationality of the beta constants L(2n, χ) are derived from the known rrationality of the zeta constants ζ(2n).

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“…contains infinitely many irrational zeta constants, see [8]. Various advanced techniques for studying the zeta constants are surveyed in [28], and [37].…”

Section: Introductionmentioning

confidence: 99%

Irrationality of the Zeta Constants

Carella

2012

Preprint

View full text Add to dashboard Cite

show abstract

Construction of Approximations to Zeta-Values

Cited by 1 publication

References 7 publications

Irrationality of the Zeta Constants

Irrationality of the Zeta Constants

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