For more information about this meeting, contact Robert Vaughan.

Title: | Dickson Polynomials over Finite Fields: a different perspective |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Gary Mullen, The Pennsylvania State University |

Abstract: |

If a is in F_q, the finite field of order q, the Dickson polynomial of degree n
and parameter a is defined by
D_n(x,a) = \sum _{i=0} ^{\lfloor n/2 \rfloor} \frac {n} {n-i} {n-i
\choose i} (-a)^i x^{n-2i}.
Dickson polynomials over finite fields have many very interesting properties,
expecially related to permutations of finite fields. In previous work, the
parameter a has been fixed and the variable x then runs through the field F_q.
In our current work, we reverse these roles, and fix x in F_q, and then allow a
to run through the elements of the field F_q. It appears that once again, we
have an interesting, though far from understood, class of polynomials.
This is joint work with James Sellers (Penn State) and Joe Yucas (Southern Illinois). |

### Room Reservation Information

Room Number: | MB106 |

Date: | 12 / 06 / 2007 |

Time: | 11:15am - 12:05pm |