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On the Number of Zeros of Diagonal Quartic Forms Over Finite Fields by Junyong Zhao; Yulu Feng; Shaofang Hong; Chaoxi Zhu is a Mathematics article available to read on EtoBox.
What is On the Number of Zeros of Diagonal Quartic Forms Over Finite Fields about?
Let F q be the finite field of q = p m ≡ 1 (mod 4) elements with p being an odd prime and m being a positive integer. For c, y ∈ F q with y ∈ F \* q non-quartic, let N n (c) and M n (y) be the numbers of zeros of In 1979, Myerson used Gauss sums and exponential sums to show that the generating function ∑ ∞ n=1 N n (0)x n is a rational function in x and presented its explicit expression. In this paper, we make use of the cyclotomic theory and exponential sums to show that the generating functions are rational functions in x. We also obtain the explicit expressions of these generating functions. Our result extends Myerson's theorem gotten in 1979.
Who reads On the Number of Zeros of Diagonal Quartic Forms Over Finite Fields?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Junyong Zhao; Yulu Feng; Shaofang Hong; Chaoxi Zhu
- Publisher
- Walter de Gruyter GmbH
- Published
- 2022
- Language
- EN
- Field
- Mathematics (Physical Sciences)