## Irreducible Polynomials of Given Forms (1999)

by
Shuhong Gao
,
Jason Howell
,
Daniel Panario

Citations: | 7 - 4 self |

### BibTeX

@MISC{Gao99irreduciblepolynomials,

author = {Shuhong Gao and Jason Howell and Daniel Panario},

title = {Irreducible Polynomials of Given Forms},

year = {1999}

}

### OpenURL

### Abstract

We survey under a unified approach on the number of irreducible polynomials of given forms: x + g(x) where the coefficient vector of g comes from an affine algebraic variety over Fq . For instance, all but 2 log n coefficients of g(x) are prefixed. The known results are mostly for large q and little is know when q is small or fixed. We present computer experiments on several classes of polynomials over F 2 and compare our data with the results that hold for large q. We also mention some related applications and problems of (irreducible) polynomials with special forms.