Représentation de \(-1\) comme somme de carrés dans un corps cyclotomique quelconque
Let \(K^{(m)}\) be the cyclotomic field of the \(m\)th roots of unity and let \(m\geq 3\) be an odd integer. The author proves that the stufe of \(K^{(m)}\) (the least number of squares necessary to represent \(-1\) in \(K^{(m)}\)) is 2 or 4 according as the multiplicative order of 2 modulo \(m\) is even or odd. This includes the results of \textit{P. Chowla} and \textit{S. Chowla} [J. Number Theory 2, 271--272 (1970; Zbl 0198.07403)] and \textit{P. Chowla} [J. Number Theory 1, 208--210 (1969; Zbl 0177.07401)].
scientific article; zbMATH DE number 3433979