Dear all,
The next talk is tomorrow, by Yashovardhan Singh Gautam of IIT, Roorkee. I apologize for the late notification.
There is also an announcement.
Bibekananda Maji (IIT, Indore) and Manjil Saikia (Ahmedabad University) have joined us as co-organisers of the SF and NT Seminar. Their interests are in Combinatorics, Number Theory and Partitions. Both have spoken in the seminar previously.
Talk Announcement:
Title: On special values of Koshliakov zeta functions
Title: On special values of Koshliakov zeta functions
Speaker: Yashovardhan Singh Gautam, Indian Institute of Technology, Roorkee, India
When: May 28, 2026, 4:00 PM- 5:00 PM IST
Where: Zoom. Write to sfandnt@gmail.com for the link
Abstract
In this talk, we study the Koshliakov zeta function ηp(s), whose theory appears to be more involved than that of its counterpart ζp(s), owing to the fact that its defining series is not of Dirichlet type. We derive formulas for ηp(s) at both even and odd values of s. In the limiting case p → ∞, our results yield the celebrated formulas of Euler and Ramanujan for the Riemann zeta function. Moreover, our results lead to several consequences concerning closed-form expressions for Lambert series and their arithmetic properties, recovering results due to Berndt, Cauchy, Ramanujan, and others. We also propose p-analogues of the transformation formula for the classical Eisenstein series. Moreover, we introduce two families of p-analogues of Ramanujan polynomials and establish functional equations satisfied by them.
--
Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia
Special Functions and Number Theory Seminar
No comments:
Post a Comment