Geodesic
A new family of exceptional polynomials in characteristic two
Robert M. Guralnick1 ; Joel Rosenberg2 ; Michael E. Zieve3
1 Department of Mathematics<br/>University of Southern California<br/>Los Angeles, CA 90089-2532<br/>United States
2 Center for Communications Research<br/>4320 Westerra Court<br/>San Diego, CA 92121-1967
3 Department of Mathematics<br/>University of Michigan<br/>530 Church Street<br/>Ann Arbor, MI 48109-1043<br/>United States
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1361-1390.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We produce a new family of polynomials $f(X)$ over fields $k$ of characteristic $2$ which are exceptional, in the sense that $f(X)-f(Y)$ has no absolutely irreducible factors in $k[X,Y]$ except for scalar multiples of $X-Y$; when $k$ is finite, this condition is equivalent to saying that the map $\alpha\mapsto f(\alpha)$ induces a bijection on an infinite algebraic extension of $k$. Our polynomials have degree $2^{e-1}(2^e-1)$, where $e>1$ is odd. We also prove that this completes the classification of indecomposable exceptional polynomials of degree not a power of the characteristic.
DOI : 10.4007/annals.2010.172.1361

Robert M. Guralnick 1 ; Joel Rosenberg 2 ; Michael E. Zieve 3

1 Department of Mathematics<br/>University of Southern California<br/>Los Angeles, CA 90089-2532<br/>United States
2 Center for Communications Research<br/>4320 Westerra Court<br/>San Diego, CA 92121-1967
3 Department of Mathematics<br/>University of Michigan<br/>530 Church Street<br/>Ann Arbor, MI 48109-1043<br/>United States 
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Robert M. Guralnick; Joel Rosenberg; Michael E. Zieve. A new family of exceptional polynomials in characteristic two. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1361-1390. doi : 10.4007/annals.2010.172.1361. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1361/

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