On the number of solutions of systems of certain diagonal equations over finite fields

被引：1

作者：

Perez, Mariana ^{[1
,3
]}

Privitelli, Melina ^{[1
,2
]}

机构：

[1] Consejo Nacl Invest Cient & Tecn CONICET, Buenos Aires, Argentina

[2] Univ Nacl Gen Sarmiento, Inst Ciencias, JM Gutierrez 1150 B1613GSX, Buenos Aires, Argentina

[3] Univ Nacl Hurlingham, Inst Tecnol Ingn, Ave Gdor Vergara 2222 B1688GEZ Villa Tesei, B1688GEZ Buenos Aires, Argentina

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 236卷

关键词：

Finite fields; Systems of diagonal equations; Rational solutions; Complete intersections; Singular locus; COVERING RADIUS; POINTS;

D O I：

10.1016/j.jnt.2021.07.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we obtain explicit estimates and existence results on the number of F-q-rational solutions of certain systems defined by families of diagonal equations over finite fields. Our approach relies on the study of the geometric properties of the varieties defined by the systems involved. We apply these results to a generalization of Waring's problem and the distribution of solutions of congruences modulo a prime number. (C)& nbsp;2021 Elsevier Inc. All rights reserved.

引用

页码：160 / 187

页数：28

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