Wednesday, March 29, 2023

Christophe Vignat (Tulane) - Thursday, Mar 30 - 4:00 PM

 The next talk is by Christophe Vignat.   It will be at our usual time of 4 PM IST. 

Talk Announcement: 

Title: Dirichlet Series Under Standard Convolutions: Variations on Ramanujan’s Identity for Odd Zeta Values 

Speaker: Christophe Vignat (Universit√© Paris-Saclay, CentraleSupelec, Orsay, France and Tulane University)
When: Mar 30, 2023, 4:00 PM- 5:00 PM IST (1:30 PM EEST)
Where: Zoom. Write to the organisers for a link.


I will show a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; this formula is inspired by a famous identity of Ramanujan.  Some specializations of this convolution formula produce new identities and allow to recover several identities derived earlier in the literature, such as the convolution of squares of Bernoulli numbers by A. Dixit and his collaborators, or the convolution of Bernoulli numbers by Y. Komori and his collaborators. 

If time permits, I will also exhibit some matrix product representations for the Riemann zeta function evaluated at even and odd integers.

This is joint work with P. Chavan, S. Chavan and T. Wakhare.

Saturday, March 11, 2023

Bruce Berndt (UIUC) - Thurs Mar 16 - 6:00 PM (Note Special Time)

 Dear all,

We are happy to announce our next talk is by Professor Bruce Berndt, the world's biggest authority on Ramanujan's mathematics and related areas. 

Please note the special time. It is two hours later than usual. Please circulate this announcement in your department. 

Please see a further announcement below.

Talk Announcement: 

Title: Finite Trigonometric Sums: Evaluations, Estimates, Reciprocity Theorems

Speaker: Bruce Berndt (University of Illinois at Urbana Champaign)
When: Mar 16, 2022, 6:00 PM- 7:00 PM IST (7:30 AM - 8:30 AM (CDT))
Where: Zoom. Please write to the organisers for the link.

First, motivated by a theorem in Ramanujan's lost notebook, Martino Fassina, Sun Kim, Alexandru Zaharescu, and the speaker developed representations for finite sums of products of trig functions for which we provided theorems and several conjectures.   

Second, a paper of Richard McIntosh served as motivation.  First, he made a very interesting conjecture, which was recently proved by Likun Xie, Zaharescu, and the speaker.  Second, he examined a particular trigonometric sum, which inspired Sun Kim, Zaharescu, and the speaker to evaluate in closed form several classes of trigonometric sums, and find reciprocity theorems for others.  

New conference announcement
A new conference on algebraic combinatorics has been announced by Arvind Ayyer. It is called 
Meru Annual Combinatorics Conference
Dates: 29th to 31st May, 2023