A q-analogue for Euler’s evaluations of the Riemann zeta function View Full Text


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Article Info

DATE

2019-03

AUTHORS

Ankush Goswami

ABSTRACT

We provide a q-analogue of Euler’s formula for ζ(2k) for k∈Z+. The result generalizes a recent result of Sun who obtained q-analogues of ζ(2)=π2/6 and ζ(4)=π4/90. This also extends an earlier result of the present author who obtained a q-analogue of ζ(6)=π6/945.

PAGES

3

References to SciGraph publications

  • 1995-08. On the representation of integers as sums of triangular numbers in AEQUATIONES MATHEMATICAE
  • 2002-11. Diophantine Problems for q-Zeta Values in MATHEMATICAL NOTES
  • 2018-02-03. Partition-Theoretic Formulas for Arithmetic Densities in ANALYTIC NUMBER THEORY, MODULAR FORMS AND Q-HYPERGEOMETRIC SERIES
  • Journal

    TITLE

    Research in Number Theory

    ISSUE

    1

    VOLUME

    5

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40993-018-0141-y

    DOI

    http://dx.doi.org/10.1007/s40993-018-0141-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1108042701


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