The sextic period polynomial
Let g be a primitive root of the prime \(p=ef+1\) and let \(\xi =\exp(2\pi i/p)\). The e periods \(\eta_ i\) are defined by \(\eta_ i=\sum^{f- 1}_{v=0}\xi^{g^{ev+i}}\quad(0\leq i\leq e-1).\) The period polynomial is the polynomial with roots \(\eta_ 0,\eta_ 1,...,\eta_{e-1}\). For \(e=6\) the authors give explicit expressions for the coefficients of the period polynomial, as well as its discriminant, in terms of the quadratic partitions \(4p=L^ 2+27M^ 2\) and \(p=A^ 2+3B^ 2.\) This paper fills a gap in the existing literature and should be useful to researchers in cyclotomy.
scientific article; zbMATH DE number 3857237