This event is from the archives of The Notice Board. The event has already taken place and the information contained in this post may no longer be relevant or accurate.
Lethbridge Number Theory and Combinatorics Seminar
Lecturer(s): Selcuk Aygin (University of Lethbridge)
Date: February 3, 2020
Time: 12:00-12:50pm
Location: C620 University Hall, University of Lethbridge
Topic: On the eta quotients whose derivatives are also eta quotients
Description:
In classical q-series studies, there are examples of eta quotients whose derivatives are also eta quotients. The most famous examples can be found in the works of S. Ramanujan and N. Fine. In 2019, in a joint work with P. C. Toh, we have given 203 pairs of such eta quotients, which we believe to be the complete list (see "When is the derivative of an eta quotient another eta quotient?", J.
Math. Anal. Appl. 480 (2019) 123366). Recently, D. Choi, B. Kim and S. Lim have given a complete list of such eta quotients with squarefree levels (see "Pairs of eta-quotients with dual weights and their applications", Adv. Math. 355
(2019) 106779). Their findings support the idea that our list is complete.
In this talk, we introduce a beautiful interplay between eta quotients, their derivatives and Eisenstein series. Then we share our work in progress (joint with A. Akbary) in proving the completeness of our list beyond squarefree levels.
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science/number-theory-combinatorics-seminars
