Date of Award
Doctor of Philosophy (PhD)
This work deals with the Fourier transform over finite fields. A notion of minimal function for the Fourier transform is defined. The minimal functions are shown to be a generalization of the famous Legendre symbol $\Psi$. The minimal functions are studied here in terms of group actions, allowing both upper and lower estimates on the size of the set of all minimal functions. These estimates are sufficient to settle a conjecture of O. C. McGehee on the number of minimal functions.
Rivero, Francisco, "Group Actions on Minimal Functions Over Finite Fields." (1987). LSU Historical Dissertations and Theses. 4473.