Corpus ID: 219124347

# On the distribution of multivariate Jacobi sums.

@article{Lu2020OnTD,
title={On the distribution of multivariate Jacobi sums.},
author={Qing Lu and Weizhe Zheng},
journal={arXiv: Number Theory},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Number Theory
• Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $q^{-(m-1)/2}J(\chi_1,\dots,\chi_m)$ ($\chi_1\dotsm \chi_m$ nontrivial) is asymptotically equidistributed on the unit circle, when $\chi_1\in \mathcal{A}_1,\dots, \chi_m\in \mathcal{A}_m$ run through arbitrary sets of nontrivial multiplicative characters of $\mathbf{F}_q^\times$, if $\#\mathcal{A}_1\ge q^{\frac{1}{2}+\epsilon}$, $\#\mathcal{A}_2 \ge (\log q)^{\frac{1}{\delta}-1}$ for \$\epsilon>\delta>0… CONTINUE READING

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