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arXiv · 2201.09262

Elementary proofs of Zagier's formula for multiple zeta values and its odd variant

Li Lai·Cezar Lupu·Derek Orr
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Abstract

In this paper, we give elementary proofs of Zagier's formula for multiple zeta values involving Hoffman element and its odd variant due to Murakami. Zagier's formula was a key ingredient in the proof of Hoffman's conjecture. Moreover, using the same approach, we prove Murakami's formula for multiple $t$-values. This formula is essential in proving a Brown type result which asserts that each multiple zeta value is a $\mathbb{Q}$-linear combination of multiple $t$-values of the same weight involving $2$'s and $3$'s.

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Li Lai, Cezar Lupu, Derek Orr. 2022-01-23. Elementary proofs of Zagier's formula for multiple zeta values and its odd variant. https://arxiv.org/abs/2201.09262

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