Student Number Theory Seminar | Gian Cordana Sanjaya | Multiplicatively dependent integer vectors on a hyperplane

Gian Cordana Sanjaya, University of Waterloo

Multiplicatively dependent integer vectors on a hyperplane

In 2018, Pappalardi, Sha, Shparlinski, and Stewart counted the number of multiplicatively dependent n-tuples of algebraic integers in a fixed number field, ordered by pointwise Weil height. Extending this work, in a joint with with Afifurrahman and Iverson in 2026, we count the number of multiplicatively dependent n-tuples of rational integers lying on a hyperplane, ordered by maximum absolute value. In this talk, we will discuss about the multiplicatively dependent tuples, some motivations behind them, and how to count these tuples, leading to the main results of both papers.

MC 5479