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Binary Quartic Forms Over Fp, Daniel Thomas Kamenetsky
Binary Quartic Forms Over Fp, Daniel Thomas Kamenetsky
Theses and Dissertations
Let Vp denote the five dimensional vector space of binary quartic forms over the finite field Fp, with p a prime greater than 3. There is a natural action of the group GL1(Fp)×GL2(Fp) on Vp. This action partitions Vp into orbits, the number of which increases with p. In this thesis, we determine explicitly, for a given p, the number of orbits under the action of GL1(Fp) × GL2(Fp) on Vp. Moreover, we determine the size of each orbit and the general structure of the forms each orbit contains. We also introduce an application of understanding these orbits to the …