**Title:**On the trace of powers of Algebraic integers

**Speaker:**R. Thangadurai

**Affiliation:**Harish-Chandra Research Institute, Prayagraj

**Venue:**Seminar Hall, KSoM

**Date and Time:**June 10, 2024 [Monday] at 11:00 AM

**Abstract:**Let be a non-zero algebraic integer. In this lecture, we prove an interesting characterisation for to be a root of unity, which is an extension of a classical theorem of Kronecker. Indeed, we prove that {\it if a non-zero algebraic integer is a root of unity if and only if the sequence is bounded. Moreover, if the sequence is bounded, then it is periodic.} Thus, if a non-zero algebraic integer is not a root of unity, it is clear that the sequence is unbounded and hence we study the growth in the next result. Also, we introduce a problem of Polya and its extensions.