5 papers
On Properly -Congruent Numbers Over Real Number Fields
Sajad Salami, Arman Shamsi Zargar
The notion of -congruent numbers generalizes the classical congruent number problem. Recall that a positive integer is -congruent if it is the area of a rational triang…
The splitting fields and Generators of Shioda's elliptic surfaces (I)
Sajad Salami, Arman Shamsi Zargar
The splitting field of an elliptic surface defined over is the smallest subfield of such that ${\mathcal E}({\mathbb C}(t))\c…
Integer triangles with a rational ratio of circumcircle radius to excircle radius
Lorenz Halbeisen, Norbert Hungerbühler, Arman Shamsi Zargar
We consider the problem of finding integer triangles with a positive rational, where and are the radii of the circumcircle and an excircle, respectively. We show that…
Generators and splitting fields of certain elliptic K3 surfaces
Sajad Salami, Arman Shamsi Zargar
Let be a number field and be an elliptic curve defined over , the rational function field of the projective line , is…
Partitions into Triples with Equal Products and Families of Elliptic Curves
Ahmed El Amine Youmbai, Arman Shamsi Zargar, Maksym Voznyy
Let denote a set of triples of positive integers having the same sum and the same product . For each we establish a connection between a…