3,198 research outputs found
Torsion of elliptic curves over quadratic cyclotomic fields
In this paper we study the possible torsions of elliptic curves over and .Comment: 9 pages, to appear in Math. J. Okayama Univ
Smooth values of some quadratic polynomials
In this paper, using a method of Luca and the author, we find all values
such that the quadratic polynomials and are
200-smooth and all values such that the quadratic polynomial is
100-smooth.Comment: 12 pages, to appear in Glas. Mat. Ser. II
Complete classification of torsion of elliptic curves over quadratic cyclotomic fields
In a previous paper, the author examined the possible torsions of an elliptic
curve over the quadratic fields and .
Although all the possible torsions were found if the elliptic curve has
rational coefficients, we were unable to eliminate some possibilities for the
torsion if the elliptic curve has coefficients that are not rational. In this
note, by finding all the points of two hyperelliptic curves over
and , we solve this problem completely and thus obtain a
classification of all possible torsions of elliptic curves over
and .Comment: 6 pages, to appear in J. Number Theor
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
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