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Machide, Tomoya

Some restricted sum formulas for double zeta values. (English) Zbl 1362.11079

Proc. Japan Acad., Ser. A 89, No. 3, 51-54 (2013).
Summary: We give some restricted sum formulas for double zeta values whose arguments satisfy certain congruence conditions modulo 2 or 6, and also give an application to identities showed by Ramanujan for sums of products of Bernoulli numbers with a gap of 6.

Cited in 3 Documents

MSC:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11B68 Bernoulli and Euler numbers and polynomials

Keywords:

multiple zeta value; double zeta value; sum formula; Bernoulli number; Ramanujan’s identity
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\textit{T. Machide}, Proc. Japan Acad., Ser. A 89, No. 3, 51--54 (2013; Zbl 1362.11079)
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References:

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[2] L. Euler, Meditationes circa singulare serierum genus, Novi Comm. Acad. Sci. Petropol. 20 (1775), 140-186, reprinted in Opera omnia , ser. I, vol. 15, Teubner, Berlin, 1927, pp. 217-267.
[3] H. Gangl, M. Kaneko and D. Zagier, Double zeta values and modular forms, in Automorphic forms and zeta functions , World Sci. Publ., Hackensack, NJ, 2006, pp. 71-106. · Zbl 1122.11057
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[5] Y. Ohno and W. Zudilin, Zeta stars, Commun. Number Theory Phys. 2 (2008), no. 2, 325-347. · Zbl 1228.11132
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