Mathematical analysis reveals statistical independence and novel Chebyshev bias in horizontal Kloosterman sums, highlighting differences from elliptic curve distributions.
In this paper, we investigate pseudorandomness of the horizontal distributions of Kloosterman sums. We conjecture that the horizontal distributions are statistically independent with respect to the Sato-Tate measure. Numerical evidence is presented to support the conjectures. We also investigate Chebyshev bias for these exponential sums, where new phenomenon shows up in comparison of Chebyshev bias for elliptic curves.
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Mok et al. (2026) studied this question.
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