Dear all,
We have a talk this week by Aritram Dhar, of the University of Florida. The title and abstract are below.
Talk Announcement:
Title: Extension of Bressoud's generalization of Borwein's conjecture, some exact results, and applications
Title: Extension of Bressoud's generalization of Borwein's conjecture, some exact results, and applications
Speaker: Aritram Dhar (University of Florida)
When: December, 2025, 4:00 PM- 5:00 PM IST
Where: Zoom. Write to the organisers for a link
Abstract:
In this talk, we conjecture an extension of Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative q-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Using certain positivity-preserving transformations for q-binomial coefficients due to Berkovich and Warnaar, we prove the non-negativity of the infinite families. Time permitting, we present some applications of cubic positivity-preserving transformations where we establish new identities analogous to Andrews' representations of the Borwein polynomials. This is based on recent joint works with Alexander Berkovich.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
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