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.2010 Mathematics Subject Classification. Primary 11M32, Secondary 40B05.
In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, such as Mordell-Tornheim type of multiple zeta values, zeta values of the root systems and so on. Moreover, we can give an explicit expression in terms of lower series by using the main theorem.
In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, such as the Mordell-Tornheim type of multiple zeta values, zeta values of the root systems and so on. Moreover, we can give an explicit expression in terms of lower series by using the main theorem.
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