## Tokyo Journal of Mathematics

### On the Parity Conjecture for Multiple $L$-values of Conductor Four

Hirofumi TSUMURA

#### Abstract

In this paper, we prove that the multiple $L$-value of conductor $4$ can be expressed in terms of lower depth multiple $L$-values under the condition on the parity of its depth and weight. This can be regarded as a character analogue of what is called the "parity result" for multiple zeta values which was proved by Zagier.

#### Article information

Source
Tokyo J. Math., Volume 30, Number 1 (2007), 21-40.

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.tjm/1184963645

Digital Object Identifier
doi:10.3836/tjm/1184963645

Mathematical Reviews number (MathSciNet)
MR2328053

Zentralblatt MATH identifier
1207.11095

#### Citation

TSUMURA, Hirofumi. On the Parity Conjecture for Multiple $L$-values of Conductor Four. Tokyo J. Math. 30 (2007), no. 1, 21--40. doi:10.3836/tjm/1184963645. https://projecteuclid.org/euclid.tjm/1184963645

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