From the 2-1 formula for multiple zeta values to iterated beta integrals

Abstract: A multiple zeta value, or MZV in short, is a generalization of the Riemann zeta value at a positive integer, defined by a certain nested infinite sum. It is well known that MZV's satisfy a large family of linear/algebraic relations over the rationals. Among such relations is the so-called two-one formula, which was first conjectured by Ohno and Zudilin as a generalization of their formula and was later proved by Zhao in a quite ingenious but also mysterious way. In my talk, I would like to revisit the two-one formula from the viewpoint of iterated beta integrals introduced by Hirose and myself. Our new viewpoint provides a clear understanding of the phenomena as well as a universal way to prove identities of similar flavors, such as Zagier’s 2-3-2 formula and its generalization.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October