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**Title**

**Speaker**

**Time**

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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.

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**Speaker**

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Stahl's theorem on a Riemann surface, Part III

E. A. Rakhmanov

4:00pm--5:00pm

CMC 130

**Title**

**Speaker**

**Time**

**Place**

Stahl's theorem on a Riemann surface, Part II

E. A. Rakhmanov

4:00pm--5:00pm

CMC 130

**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.