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.
the maximal coefficient (in absolute value) of the cyclotomic polynomial
be three prime numbers.
In this case the cyclotomic polynomial
is called ternary.
In 1895, A. S. Bang[2] proved that
This implies the existence of
{\displaystyle M(p):=\max \limits _{p\leq q\leq r{\text{ prime}}}A(pqr)}
Sister Beiter conjectured[1] in 1968 that
This was later disproved, but a corrected Sister Beiter conjecture was put forward as
A preprint[3] from 2023 explains the history in detail and claims to prove this corrected conjecture.
Explicitly it claims to prove