Dear all,
The talk this week is by Nikita Kalinin, Guangdong Technion Israel Institute of Technology, Shantou, China.
Talk Announcement:
Title: Evaluation of lattice sums via telescoping over topographs
Title: Evaluation of lattice sums via telescoping over topographs
Speaker: Nikita Kalinin, Guangdong Technion Israel Institute of Technology, Shantou, China.
When: Feb 19, 2026, 4:00 PM- 5:00 PM IST (1830 Beijing Time)
When: Feb 19, 2026, 4:00 PM- 5:00 PM IST (1830 Beijing Time)
Where: Zoom: write to the organsers for the link
Abstract
Conway’s topograph provides a geometric way to organize values of binary quadratic forms on an infinite trivalent planar tree. In this talk, I explain how summation over vertices and edges of a topograph leads to a systematic method for evaluating a broad class of lattice sums by telescoping.
The main idea is that many arithmetic sums indexed by primitive lattice points or Farey-type data admit a natural decomposition along oriented edges of the topograph. When written in this form, local identities at each vertex produce global cancellations, yielding exact closed formulas depending only on the root configuration and the discriminant. This viewpoint unifies and simplifies several known identities, including sums related to reciprocal products of quadratic form values, Mordell–Tornheim–type series, and formulas connected to Euler-type constants.
The talk will be largely elementary and geometric. I will introduce the necessary background on topographs, explain the telescoping mechanism in a concrete way, and illustrate how classical analytic identities emerge from purely combinatorial summation over the tree.
The talk is based on https://arxiv.org/abs/2510.
The talk is based on https://arxiv.org/abs/2510.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
