E-mail
komer@metu.edu.tr
Department
Department of Mathematics
Scopus Author ID
Value sets of folding polynomials over finite fields
Küçüksakallı, Ömer (2019-01-01)
Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x...
Value sets of bivariate folding polynomials over finite fields
Küçüksakallı, Ömer (2018-11-01)
We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras B-2 and G(2) over finite fields. We achieve this by using a characterization of their fixed points in terms of sums o...
Arithmetic exceptionality of generalized Lattes maps
Küçüksakallı, Ömer; Önsiper, Mustafa Hurşit (2018-04-01)
We consider the arithmetic exceptionality problem for the generalized Lattes maps on P-2. We prove an existence result for maps arising from the product E x E of elliptic curves E with CM.
On the arithmetic exceptionality of polynomial mappings
Küçüksakallı, Ömer (2018-02-01)
In this note we prove that certain polynomial mappings P-g(k) (x) is an element of Z[x] in n-variables obtained from simple complex Lie algebras g of arbitrary rank n1, are exceptional.
A Proof of the Lucas-Lehmer Test and its Variations by Using a Singular Cubic Curve
Küçüksakallı, Ömer (2018-01-01)
We give another proof of the Lucas-Lehmer test by using a singular cubic curve. We also illustrate a practical way to choose a starting term for the Lucas-Lehmer-Riesel test by trial and error. Moreover, we provide a nonde...
Bivariate polynomial mappings associated with simple complex Lie algebras
Küçüksakallı, Ömer (2016-11-01)
There are three families of bivariate polynomial maps associated with the rank-2 simple complex Lie algebras A(2), B-2 congruent to C-2 and G(2). It is known that the bivariate polynomial map associated with A(2) induces a...
Value sets of bivariate Chebyshev maps over finite fields
Küçüksakallı, Ömer (2015-11-01)
We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of ro...
On the computation of generalized division polynomials
Küçüksakallı, Ömer (2015-01-01)
We give an algorithm to compute the generalized division polynomials for elliptic curves with complex multiplication. These polynomials can be used to generate the ray class fields of imaginary quadratic fields over the Hi...
Value sets of Lattes maps over finite fields
Küçüksakallı, Ömer (Elsevier BV, 2014-10-01)
We give an alternative computation of the value sets of Dickson polynomials over finite fields by using a singular cubic curve. Our method is not only simpler but also it can be generalized to the non-singular elliptic cas...
On the units generated by Weierstrass forms
Küçüksakallı, Ömer (2014-01-01)
There is an algorithm of Schoof for finding divisors of class numbers of real cyclotomic fields of prime conductor. In this paper we introduce an improvement of the elliptic analogue of this algorithm by using a subgroup o...