Illinois Journal of Mathematics

Evaluation of Tornheim’s type of double series

Shin-ya Kadota, Takuya Okamoto, and Koji Tasaka

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Abstract

We examine values of certain Tornheim’s type of double series with odd weight. As a result, an affirmative answer to a conjecture about the parity theorem for the zeta function of the root system of the exceptional Lie algebra $G_{2}$, proposed by Komori, Matsumoto and Tsumura, is given.

Article information

Source
Illinois J. Math., Volume 61, Number 1-2 (2017), 171-186.

Dates
Received: 29 March 2017
Revised: 3 September 2017
First available in Project Euclid: 3 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1520046214

Digital Object Identifier
doi:10.1215/ijm/1520046214

Mathematical Reviews number (MathSciNet)
MR3770841

Zentralblatt MATH identifier
06864464

Subjects
Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values
Secondary: 40B05: Multiple sequences and series (should also be assigned at least one other classification number in this section)

Citation

Kadota, Shin-ya; Okamoto, Takuya; Tasaka, Koji. Evaluation of Tornheim’s type of double series. Illinois J. Math. 61 (2017), no. 1-2, 171--186. doi:10.1215/ijm/1520046214. https://projecteuclid.org/euclid.ijm/1520046214


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References

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