Abstract
We prove analogs of the Burgess estimates for character sums over n-dimensional segments in the field \( \mathbb{F}_{p^n } \).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. A. Burgess, “On character sums and primitive roots,” Proc. London Math. Soc. (3) 12, 179–192 (1962).
D. A. Burgess, “Character sums and primitive roots in finite fields,” Proc. Lond. Math. Soc. (3) 17, 11–25 (1967).
A. A. Karatsuba, “Character sums and primitive roots in finite fields,” Dokl. Akad. Nauk SSSR 180(6), 1287–1289 (1968) [SovietMath. Dokl. 9, 755–757 (1968)].
A. A. Karatsuba, “On estimates of character sums,” Izv. Akad. Nauk SSSR Ser. Mat. 34(1), 20–30 (1970) [Math. USSR-Izv. 4, 19–29 (1970)].
H. Davenport and D. J. Lewis, “Character sums and primitive roots in finite fields,” Rend. Circ. Mat. Palermo (2) 12(2), 129–136 (1963).
M.-Ch. Chang, “On a question of Davenport and Lewis and new character sum bounds in finite fields,” Duke Math. J. 145(3), 409–442 (2008).
M.-Ch. Chang, Burgess Inequality in \( \mathbb{F}_{p^2 } \), Preprint, 2009.
T. Tao and V. Vu, Additive Combinatorics, in Cambridge Stud. Adv. Math. (Cambridge Univ. Press, Cambridge, 2006), Vol. 105.
W. Banaszczyk, “Inequalities for convex bodies and polar reciprocal lattices in ℝn,” Discrete Comput. Geom. 13(2), 217–231 (1995).
W. M. Schmidt, Equations over Finite Fields: An Elementary Approach, in Lecture Notes in Math. (Springer-Verlag, Berlin, 1976), Vol. 536.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S. V. Konyagin, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 4, pp. 529–542.
Rights and permissions
About this article
Cite this article
Konyagin, S.V. Estimates of character sums in finite fields. Math Notes 88, 503–515 (2010). https://doi.org/10.1134/S0001434610090221
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434610090221