Corrected Beiter conjecture for ternary cyclotomic heights

About 19 years old · traced to

For each prime pp, define

M(p):=max⁡p<q<r primesA(pqr),M(p):=\max_{p<q<r\text{ primes}} A(pqr),

\nwhere A(n)A(n) is the height of the cyclotomic polynomial Φn\Phi_n.

Corrected Beiter conjecture. Moree and Gallot proposed that

M(p)≤23p.M(p)\leq \frac{2}{3}p.

This is the corrected weaker form of Beiter's conjecture after the original bound was disproved for all primes p≥11p\geq 11. The paper presents a proof of this bound, so the conjecture is solved.

References

Primary source

Branko Juran, Pieter Moree, Adrian Riekert, David Schmitz and Julian Völlmecke, “A proof of the corrected Sister Beiter cyclotomic coefficient conjecture inspired by Zhao and Zhang”, arXiv:2304.09250 (2023).

Additional references

4 papers in this index state this conjecture (2007–2023). The statement above is taken from the most recent of them; the others are arXiv:0910.2770, arXiv:0910.1982, arXiv:0712.2365.

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.