ICTS:32149

Video URL

Summation Formulas: From Classical Foundations to Harmonic Maass Forms

Summation Formulas: From Classical Foundations to Harmonic Maass Forms

(2025). Summation Formulas: From Classical Foundations to Harmonic Maass Forms. SciVideos. https://youtube.com/live/Unlt-kPS_nQ

Summation Formulas: From Classical Foundations to Harmonic Maass Forms. SciVideos, Jul. 02, 2025, https://youtube.com/live/Unlt-kPS_nQ 

          @misc{ scivideos_ICTS:32149,
            doi = {},
            url = {https://youtube.com/live/Unlt-kPS_nQ},
            author = {},
            keywords = {},
            language = {en},
            title = {Summation Formulas: From Classical Foundations to Harmonic Maass Forms},
            publisher = {},
            year = {2025},
            month = {jul},
            note = {ICTS:32149 see, \url{https://scivideos.org/icts-tifr/32149}}
          }
Rajat Gupta
Talk numberICTS:32149
Source RepositoryICTS-TIFR

Abstract

In the first part of this talk, I will provide a brief introduction to classical summation formulas and their significance in number theory. We will review the foundational contributions of Bochner, Koshliakov, and the seminal work of Chandrasekharan and Narasimhan on summation formulas for a broad class of arithmetical functions.

In the second part, I will present recent developments involving new summation formulas in the theory of harmonic Maass forms. As an application of our summation formula, I will discuss the asymptotic behavior of the Riesz means of the Hurwitz class numbers.\\

This talk is based on recent joint work with Olivia Beckwith, Nikolaos Diamantis, Larry Rolen, and Kalani Thalagoda.