## Thursday, April 29, 2021

### R Balasubramanian (I.M.Sc., Chennai) April 29, 2021 - 3:55 PM - 5:00 PM (IST)

Talk Announcement:

Title: Hardy's approximation to the Riemann Zeta Function

Speaker: Professor R Balasubramanian (IMSc, Chennai)

When: April 29, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom

## Thursday, April 15, 2021

### Nayandeep Deka Baruah (Tezpur University) - April 15, 2021 - 3:55 PM-5:00 PM (IST)

Our next speaker is Nayandeep Deka Baruah of Tezpur University, Assam, India.

Talk Announcement:

Title: Matching coefficients in the series expansions of certain $q$-products and their inverses.

Speaker: Nayandeep Deka Baruah (Tezpur University)

When: April 15, 2021 - 3:55 PM - 5:00 PM (IST)

Abstract:We show that the series expansions of certain  $q$-products have \textit{matching coefficients} with their inverses. Several of the results are associated to Ramanujan's continued fractions. For example, let $R(q)$ denote the Rogers-Ramanujan continued fraction having the well-known $q$-product repesentation $R(q)=\left(q,q^4;q^5\right)_{\infty}/\left(q^2,q^3;q^5\right)_{\infty}$. If
\begin{align*}
\sum_{n=0}^{\infty}\alpha(n)q^n=\dfrac{1}{R^5\left(q\right)}=\left(\sum_{n=0}^{\infty}\alpha^{\prime}(n)q^n\right)^{-1},\\
\sum_{n=0}^{\infty}\beta(n)q^n=\dfrac{R(q)}{R\left(q^{16}\right)}=\left(\sum_{n=0}^{\infty}\beta^{\prime}(n)q^n\right)^{-1},
\end{align*}
then
\begin{align*}
\alpha(5n+r)&=-\alpha^{\prime}(5n+r-2), \quad r\in\{3,4\}; \\ \text{and} & \\
\end{align*}
This is a joint work with Hirakjyoti Das.

## Thursday, April 1, 2021

### Shishuo Fu (Chongqing University, PRC) - April 1, 2021 - 3:55 PM - 5:00 PM (IST)

The next speaker in our seminar is Shishuo Fu of Chongqing University, PRC. It may be Fool's day, but we're not kidding. It really is Shishuo who has consented to give a talk all the way from China!

The live broadcast did not work as anticipated in the previous talk; I hope it works this time. At any rate, its best to try and come for the zoom session.

Talk Announcement

Title: Bijective recurrences for Schroeder triangles and Comtet statistics

Speaker: Shishuo Fu (Chongqing University, PRC)

When: April 1, 2021 - 3:55 PM - 5:00 PM (IST)