4 papers
Graph of even points on an arithmetic curve
Alfred Czogała, Przemysław Koprowski
We show that the points of a global function field, whose classes are 2-divisible in the Picard group, form a connected graph, with the incidence relation generalizing the well kno…
Wild sets in global function fields
Alfred Czogała, Przemysław Koprowski, Beata Rothkegel
Given a self-equivalence of a global function field, its wild set is the set of points where the self-equivalence fails to preserve parity of valuation. In this paper we describe s…
Yet another proof of the quadratic reciprocity law
Alfred Czogała, Przemysław Koprowski
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
Computing with quadratic forms over number fields
Przemysław Koprowski, Alfred Czogała
This paper presents fundamental algorithms for the computational theory of quadratic forms over number fields. In the first part of the paper, we present algorithms for checking if…