11 citations · 44 across the 10 of their papers we have counts for
10 papers
Explicit estimates for polynomial systems defining irreducible smooth complete intersections
Joachim von zur Gathen, Guillermo Matera
This paper deals with properties of the algebraic variety defined as the set of zeros of a "typical" sequence of polynomials. We consider various types of "nice" varieties: set-the…
Survey on counting special types of polynomials
Joachim von zur Gathen, Konstantin Ziegler
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gauß count the remaining ones, app…
Density of real and complex decomposable univariate polynomials
Joachim von zur Gathen, Guillermo Matera
We estimate the density of tubes around the algebraic variety of decomposable univariate polynomials over the real and the complex numbers.
Circulant graphs and GCD and LCM of Subsets
Joachim von zur Gathen, Igor E. Shparlinski
Given two sets and of integers, we consider the problem of finding a set of the smallest possible cardinality such the greatest common divisor of the elemen…
Normal form for Ritt's Second Theorem
Joachim von zur Gathen
Ritt's Second Theorem deals with composition collisions g o h = g* o h* of univariate polynomials over a field, where deg g = deg h*. Joseph Fels Ritt (1922) presented two types of…
The number of reducible space curves over a finite field
Eda Cesaratto, Joachim von zur Gathen, Guillermo Matera
"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. Th…