Feb. 1, 3:30pm, Wean 8220

Cezar Lupu, University of Pittsburgh

Multiple zeta values: analytic and combinatorial aspects

Cezar Lupu, University of Pittsburgh

Multiple zeta values: analytic and combinatorial aspects

Abstract:

The multiple zeta values (Eulerâ€“Zagier sums) were introduced independently by Hoffman and Zagier in 1992 and they play a crucial role at the interface between analysis, number theory, combinatorics, algebra and physics.

The central part of the talk is given by Zagier's formula for the multiple
zeta values, ζ(*2*, *2*,..., *2*, *3*, *2*, *2*,..., *2*). Zagier's formula
is a remarkable example of both strength and the limits of the motivic
formalism used by Brown in proving Hoffman's conjecture where the motivic
argument does not give us a precise value for the special multiple zeta
values ζ(*2*, *2*,..., *2*, *3*, *2*, *2*,..., *2*) as rational linear
combinations of products ζ(*m*)π^{2n} with *m* odd.
The formula is proven indirectly by computing the generating functions of
both sides in closed form and then showing that both are entire functions
of exponential growth and that they agree at sufficiently many points to
force their equality.

By using the Taylor series of integer powers of `arcsin` function and a
related result about expressing rational zeta series involving ζ(*2n*)
as a finite sum of **Q**-linear combinations of odd zeta values and
powers of π, we derive a new and direct proof of Zagier's formula in
the special case ζ(*2*, *2*,..., *2*, *3*).

Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.