On the coming Thursday, Atul Dixit (IIT, Gandhinagar) and Gaurav Bhatnagar (Ashoka University) will present the talks they presented at the recently concluded JMM meeting held online. Each talk will be approximately 20 minutes followed by 10 minutes for questions. The titles and abstracts are below.
Here is the announcement for the second talk of the day.
Title: An easy proof of Ramanujan's famous mod $5$ congruences
Speaker: Gaurav Bhatnagar (Ashoka University)
When: Thursday, April 21, 2022 - 4:30 PM - 5:00 PM
Where: Zoom.
Live LInk: https://youtu.be/IB3FiBM2j5s
Abstract
We give an elementary proof of Ramanujan's famous congruences $p(5n+4) \equiv 0 \mod 5$ and $\tau(5n+5)\equiv 0 \mod 5$. The proof requires no more than Euler's techniques and a result of Jacobi. The proof extends to embed the congruences into 4 infinite families of congruences for rational powers of the eta function.
This is joint work with Hartosh Singh Bal.
The video below is the same as the one in Atul's talk. It just begins in the middle.
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