Abstract
For a nontrivial additive character λ of the finite field with q elements and each positive integer r, the exponential sums ∑ λ ( ( trw )r ) over w ∈ SO +(2n,q) and over w ∈ O +(2n,q) are considered. We show that both of them can be expressed as polynomials in q involving certain new exponential sums. Estimates on those new exponential sums are given. Also, we derive from these expressions the formulas for the number of elements w in SO +(2n,q) and O +(2n,q) with (trw)r = β, for each β in the finite field with q elements.
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Kim, D.S. Exponential Sums for O+(2n,q) and Their Applications. Acta Mathematica Hungarica 91, 79–97 (2001). https://doi.org/10.1023/A:1010634927604
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DOI: https://doi.org/10.1023/A:1010634927604