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}
}
  • Qing Lu, Weizhe Zheng
  • 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

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 10 REFERENCES
    Application de la formule des traces aux sommes trigonométriques, Cohomologie étale
    • 1977
    Equidistributions of Jacobi sums
    1
    On a problem in the theory of uniform distribution. I, II
    • 1948
    On a problem in the theory of uniform distribution. I, II, Nederl
    • 1948
    On the distribution of Jacobi sums
    2
    On the uniform distribution of Gauss sums and Jacobi sums
    • 1995
    On the uniform distribution of Gauss sums and Jacobi sums, Analytic number theory, Vol. 2 (Allerton
    • 1995