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### BIMSA一周学术活动 2022.07.11-2022.07.15    # 公开课/COURSE # 讨论班/SEMINAR

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

BIMSA-YMSC Tsinghua Number Theory Seminar

Zoom ：361 038 6975（PW: BIMSA）

In 2012, Zagier proved a formula which expresses the multiple zeta values $H(a, b)=\zeta(\underbrace{2,2, \ldots, 2}_{a}, 3, \underbrace{2,2, \ldots, 2}_{b})$ as explicit $\mathbb{Q}$-linear combinations of products $\pi^{2m}\zeta(2n+1)$ with $2m+2n+1=2a+2b+3$. Recently, Murakami proved an odd variant of Zagier's formula for the multiple $t$-values $T(a, b)=t(\underbrace{2,2, \ldots, 2}_{a}, 3, \underbrace{2,2, \ldots, 2}_{b}).$ In this talk, we will give new and parallel proofs of these two formulas. Our proofs are elementary in the sense that they only involve the Taylor series of powers of arcsine function and certain trigonometric integrals. Thus, these formulas become more transparent from the view of analysis. This is a joint work with Cezar Lupu and Derek Orr.

• ### BIMSA一周学术活动 2022.07.04-2022.07.08

公开课/COURSE讨论班/SEMINAR2022-07-05 Elementary proofs of Zagier's formula for multiple zeta values and its odd variantBIMSA-YMSC Tsinghua Number Theory Seminar报告人 赖力 清华大学时 间 16:00-17:00 Tue地 点 1110Zoom 361 038 6975（PW: BIMSA）摘要In 2012, Zagier proved a formula which expresses the multiple zeta values \[ H(a, b)=\zeta(\underbrace{2,2, \ldots, 2}_{a}, 3, \underbrace{2,2, \ldots...

• ### 【2022-11-30 17:15】Geometry & Gravitation

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