Anup Dixit (IMSc, Chennai) - July 22, 2021 - 3:55 PM - 5:00 PM (IST)

The next speaker in the SF and NT Seminar is Anup Biswanath Dixit of IMSc. (Chennai). Here is the announcement.

Talk Announcement:

Title: On Euler-Kronecker constants and the class number problem

Speaker: Anup Dixit (IMSc, Chennai)

 

When: Thursday, July 22, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom (please send email to sfandnt@gmail.com for a link)

 

Live Link: https://youtu.be/XGD-oh-WkPA

Tea or Coffee: Please bring your own.

 Abstract:  

As a natural generalization of the Euler's constant 
$\gamma$, Y. Ihara introduced the Euler-Kronecker constants attached 
to any number field. In this talk, we will discuss the connection 
between these constants and certain arithmetic properties of number 
fields.

Bibekananda Maji (IIT, Indore) - July 8, 2021 - 3:55 PM - 5:00 PM (IST)

 Dear all,

The next talk is by Bibekananda Maji of IIT, Indore. Here is the announcement.

Talk Announcement:

Title: On Ramanujan's formula for $\zeta(1/2)$ and $\zeta(2m+1)$

Speaker: Bibekananda Maji (IIT, Indore)

 

When: Thursday, July 8, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom (please send email to sfandnt@gmail.com for a link)

 

Live Link: https://youtu.be/_GSUW18gSo4

Tea or Coffee: Please bring your own.

Abstract: 

Euler's remarkable formula for $\zeta(2m)$ immediately tells us that even zeta values are transcendental. However, the algebraic nature of odd zeta values is yet to be determined.  Page 320 and 332 of Ramanujan's Lost Notebook contains an intriguing identity for $\zeta(2m+1)$ and $\zeta(1/2)$, respectively.  Many mathematicians have studied these identities over the years.

In this talk, we shall discuss transformation formulas for a certain infinite series,  which will enable us to derive Ramanujan's formula for $\zeta(1/2),$ Wigert's formula for $\zeta(1/k)$, as well as Ramanujan's formula for $\zeta(2m+1)$. We also obtain a new identity for $\zeta(-1/2)$ in the spirit of Ramanujan.

This is joint work with Anushree Gupta.