Seminar:
Algebra and Number Theory Seminar
Event time:
Tuesday, April 5, 2022 - 4:30pm
Speaker:
Cezar Lupu
Speaker affiliation:
Beijing Institute of Mathematical Sciences and Applications (BIMSA) & Yau Mathematical Sciences Center (YMSC), Tsinghua University
Event description:
In this talk, we revisit the famous Zagier formula for multiple zeta values (MZV’s) and its odd variant for multiple t-values which is due to Murakami.
Zagier’s formula involves a specific family of MZV’s which we call nowadays the Hoffman family, which can be expressed as a Q-linear combination of products π2mζ(2n+1) with m+n=a+b+1. This formula for H(a,b) played a crucial role
in the proof of Hoffman’s conjecture by F. Brown, and it asserts that all multiple zeta values of a given weight are Q-linear combinations of MZV’s of the same weight involving 2’s and 3’s.
Similarly, in the case of multiple t-values (the odd variant of multiple zeta values), very recently, Murakami proved a version of Brown’s theorem (Hoffman’s conjecture) which states that every multiple zeta value is a Q-linear combination of elements. Again, the proof relies on a Zagier-type
evaluation for the Hoffman’s family of multiple t-values.
We show the parallel of the two formulas for H(a,b) and T(a,b) and derive elementary proofs by relating both of them to a surprising cotangent integral. Also, if time will allow, we give a brief account on how these integrals can provide us some arithmetic information about ζ(2k+1)π2k+1. This is a joint work with Li Lai and Derek Orr.
Research area(s):
Algebraic Geometry
Number Theory
Representation Theory