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

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

Speaker: Li Lai (Tsinghua University)

Time: 16:00-17:00 Beijing time, Jul 12, 2022

Zoom ID: 361 038 6975 Passcode: BIMSA

Room: BIMSA 1110

Abstract:

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-YMSC Tsinghua Number Theory Seminar