Sister Beiter conjecture


In mathematics, the Sister Beiter conjecture is a conjecture about the size of coefficients of ternary cyclotomic polynomials. It is named after Marion Beiter, a Catholic nun who first proposed it in 1968.

Background

For the maximal coefficient of the cyclotomic polynomial is denoted by.
Let be three prime numbers. In this case the cyclotomic polynomial is called ternary. In 1895, A. S. Bang proved that. This implies the existence of such that.

Statement

Sister Beiter conjectured in 1968 that. This was later disproved, but a corrected Sister Beiter conjecture was put forward as.

Status

A preprint from 2023 explains the history in detail and claims to prove this corrected conjecture. Explicitly it claims to prove