4 citations · 13 across the 9 of their papers we have counts for
11 papers · 1 filter
A note on the stability of trinomials over finite fields
Omran Ahmadi, Kosrov Monsef-Shokri
A polynomial over a field is called stable if all of its iterates are irreducible over . In this paper we study the stability of trinomials over finite fields. Specia…
Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients
Omran Ahmadi, Faruk Gologlu, Robert Granger +2
For any positive integers we present formulae for the number of irreducible polynomials of degree over the finite field where the coeffici…
Decomposing Jacobians of Curves over Finite Fields in the Absence of Algebraic Structure
Omran Ahmadi, Gary McGuire, Antonio Rojas-León
We consider the issue of when the L-polynomial of one curve over $\F_q$ divides the L-polynomial of another curve. We prove a theorem which shows that divisibility follows from a h…
Exponential Sums over Points of Elliptic Curves
Omran Ahmadi, Igor E. Shparlinski
We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential…
An efficient deterministic test for Kloosterman sum zeros
Omran Ahmadi, Robert Granger
We propose a simple deterministic test for deciding whether or not an element $a \in \F_{2^n}^{\times}$ or $\F_{3^n}^{\times}$ is a zero of the corresponding Kloosterman sum over t…
On isogeny classes of Edwards curves over finite fields
Omran Ahmadi, Robert Granger
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class c…
Generalization of a Theorem of Carlitz
Omran Ahmadi
We generalize Carlitz' result on the number of self reciprocal monic irreducible polynomials over finite fields by showing that similar explicit formula hold for the number of irre…
A Note on Stable Quadratic Polynomials over Fields of Characteristic Two
Omran Ahmadi
In this note, first we show that there is no stable quadratic polynomial over finite fields of characteristic two and then show that there exist stable quadratic polynomials over f…
On the Distribution of the Number of Points on Algebraic Curves in Extensions of Finite Fields
Omran Ahmadi, Igor E. Shparlinski
Let $\cC$ be a smooth absolutely irreducible curve of genus defined over $\F_q$, the finite field of elements. Let $# \cC(\F_{q^n})$ be the number of $\F_{q^n}$-ratio…
On the Sum-Product Problem on Elliptic Curves
Omran Ahmadi, Igor Shparlinski
Let $\E$ be an ordinary elliptic curve over a finite field $\F_{q}$ of elements and denote the -coordinate of a point on $\E$. Given an $\F_q$-ratio…
Multiplicative Order of Gauss Periods
Omran Ahmadi, Igor E. Shparlinski, Jose Felipe Voloch
We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of J. von zur Gathen and…