Cyclotomic polynomials with prescribed height and prime number theory

2019/10/02 by Kosyak, Alexandre, Moree, Pieter, Sofos, Efthymios +1 · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1910.01039

Abstract

Given any positive integer n, let A(n) denote the height of the n^th cyclotomic polynomial, that is its maximum coefficient in absolute value. It is well known that A(n) is unbounded. We conjecture that every natural number can arise as value of A(n) and prove this assuming that for every pair of consecutive primes p and p' with p≥ 127 we have p'-p

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• Conjectures about Primes and Cyclic Numbers

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