In mathematics, the Sister Beiter conjecture is a conjecture about the size of coefficients of ternary cyclotomic polynomials (i.e. where the index is the product of three prime numbers). It is named after Marion Beiter, a Catholic nun who first proposed it in 1968.
For the maximal coefficient (in absolute value) 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 .
Sister Beiter conjectured in 1968 that . This was later disproved, but a corrected Sister Beiter conjecture was put forward as .
A preprint from 2023 explains the history in detail and claims to prove this corrected conjecture. Explicitly it claims to prove