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Mathematics & Statistics

Analysis
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Friday, November 22, 2019

Title
Speaker

Time
Place

A Zagier-type formula for special multiple Hurwitz zeta values
Cezar Lupu
Texas Tech University
4:00pm--5:00pm
CMC 130

Abstract

In this talk, we provide a Zagier-type formula for the multiple $t$-values (special Hurwitz zeta values), \begin{gather*} t\left(k_{1},k_{2},\dotsc,k_{r}\right)=2^{-\left(k_{1}+k_{2}+\dotsb+k_{r}\right)}\zeta\left(k_{1},k_{2},\dotsc,k_{r};-\frac{1}{2},-\frac{1}{2},\dotsc,-\frac{1}{2}\right) \\ =\sum_{1\le n_{1}< n_{2}<\dotsb< n_{r}}\frac{1}{\left(2n_{1}-1\right)^{k_{1}}\left(2n_{2}-1\right)^{k_{2}}\dotsm\left(2n_{r}-1\right)^{k_{r}}}. \end{gather*}

Our formula is similar with Zagier's formulas for MZVs \(\zeta(2,\dotsc,2,3)\) and will involve \(\mathbb{Q}\)-linear combinations of powers of \(\pi\) and odd zeta values. The derivation of the formula for \(t(2,\dotsc,2,3)\) relies on a rational zeta series approach via a Gauss hypergeometric argument.

Friday, September 20, 2019

Title
Speaker
Time
Place

Stahl's theorem on a Riemann surface, Part III
E. A. Rakhmanov
4:00pm--5:00pm
CMC 130

Friday, September 13, 2019

Title
Speaker
Time
Place

Stahl's theorem on a Riemann surface, Part II
E. A. Rakhmanov
4:00pm--5:00pm
CMC 130

Friday, September 6, 2019

Title
Speaker
Time
Place

Stahl's theorem on a Riemann surface
E. A. Rakhmanov
4:00pm--5:00pm
CMC 130

Abstract

H. Stahl's theorem on convergence of Pade approximats for analytic functions with branch points is one of the fundamental results in the theory of rational approximations of analytic functions. It is also one of the basic facts in the theory of orthogonal polynomials. Denominators of Pade approximats are complex (non-hermitian) orthogonal polynomials and Stahl's created an original method of investigating asymptotics of complex orthogonal polynomials based directly on complex orthogonality.