PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

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
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