Sajad Salami

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20172026

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10 papers · 1 filter

math.NT2026

Gaussian Behavior and Geometric Gaps in Decompositions from Recurrences with Zero Coefficients

Sajad Salami

Zeckendorf's theorem establishes a unique representation for positive integers as sums of non-consecutive Fibonacci numbers. This result has been generalized to Positive Linear Rec…

math.NT2026

The splitting field and generators of the elliptic surface $Y^{2} = X^{3} + t^{360} + 1$

Sajad Salami

The splitting field of an elliptic surface $E / Q (t)$ is the smallest finite extension $K \subset C$ such that all $C (t)$ -rational poin…

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

Rank of Jacobian Varieties of Curves $y^{s} = x (a x^{r} + b)$

Sajad Salami

Let $k$ be a number field. We investigate the Mordell-Weil ranks of Jacobian varieties $J_{C}$ associated with algebraic curves $C$ of genus $g \geq 1$ defined by affine equations of…

math.NT2025

On the Rank of Jacobian Varieties of the Curves $y^{s} = a x^{r} + b$

Sajad Salami

We study the family of algebraic curves of genus $\geq 1$ defined by the affine equations $y^{s} = a x^{r} + b$ over a number field $k$ , where $r \geq 2$ and $s \geq 2$ are fixed integers. A…

Gaussian Behavior and Geometric Gaps in Decompositions from Recurrences with Zero Coefficients

The splitting field and generators of the elliptic surface Y2=X3+t360+1

On Properly θ-Congruent Numbers Over Real Number Fields

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

Rank of Jacobian Varieties of Curves ys=x(axr+b)

On the Rank of Jacobian Varieties of the Curves ys=axr+b

The splitting field and generators of the elliptic surface $Y^{2} = X^{3} + t^{360} + 1$

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)

Rank of Jacobian Varieties of Curves $y^{s} = x (a x^{r} + b)$

On the Rank of Jacobian Varieties of the Curves $y^{s} = a x^{r} + b$