Evaluation of Tornheim's type of double series

Shin-ya Kadota; Takuya Okamoto; Koji Tasaka

Evaluation of Tornheim's type of double series

Number Theory 2017-03-23 v1

Authors: Shin-ya Kadota , Takuya Okamoto , Koji Tasaka

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.

Keywords

Tornheim double series zeta function root system exceptional Lie algebra parity theorem

Cite

@article{arxiv.1703.07471,
  title  = {Evaluation of Tornheim's type of double series},
  author = {Shin-ya Kadota and Takuya Okamoto and Koji Tasaka},
  journal= {arXiv preprint arXiv:1703.07471},
  year   = {2017}
}

Comments

14 pages

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