A. S. Zargar

activity

20152025

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math.NT2025

On Properly $θ$ -Congruent Numbers Over Real Number Fields

Sajad Salami, Arman Shamsi Zargar

The notion of $θ$ -congruent numbers generalizes the classical congruent number problem. Recall that a positive integer $n$ is $θ$ -congruent if it is the area of a rational triangle…

math.NT2025

The splitting fields and Generators of Shioda's elliptic surfaces $y^{2} = x^{3} + t^{m} + 1$ (I)

Sajad Salami, Arman Shamsi Zargar

The splitting field of an elliptic surface $E$ defined over $Q (t)$ is the smallest subfield $K$ of $C$ such that ${\mathcal E}({\mathbb C}(t))\c…

math.NT2025

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 $R / r$ a positive rational, where $R$ and $r$ are the radii of the circumcircle and an excircle, respectively. We show that…

On Properly θ-Congruent Numbers Over Real Number Fields

The splitting fields and Generators of Shioda's elliptic surfaces y2=x3+tm+1 (I)

Integer triangles with a rational ratio of circumcircle radius to excircle radius

On Properly $θ$ -Congruent Numbers Over Real Number Fields

The splitting fields and Generators of Shioda's elliptic surfaces $y^{2} = x^{3} + t^{m} + 1$ (I)