Computing Singular Elements Modulo Squares

Article type: Research Article

Authors: Koprowski, Przemysław^{; *}

Affiliations: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland. [email protected]

Correspondence: [*] Address for correspondence: Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland.

Abstract: The group of singular elements was first introduced by Helmut Hasse and later it has been studied by numerous authors including such well known mathematicians as: Cassels, Furtwängler, Hecke, Knebusch, Takagi and of course Hasse himself; to name just a few. The aim of the present paper is to present algorithms that explicitly construct groups of singular and S-singular elements (modulo squares) in a global function field.

Keywords: global function fields, singular elements, square classes, Picard group

DOI: 10.3233/FI-2021-2022

Journal: Fundamenta Informaticae, vol. 179, no. 3, pp. 227-238, 2021