SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS

被引：0

作者：

Shparlinski, Igor E. ^{[1
]}

机构：

[1] Univ New S Wales, Dept Pure Math, Sydney, NSW 2052, Australia

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2016年 / 93卷 / 03期

关键词：

multiplicative congruences; resultant; common roots; PSEUDORANDOM BINARY LATTICES; K SYMBOLS; SEQUENCES; FIELDS; SUMS;

D O I：

10.1017/S0004972715001240

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an upper bound for the number of solutions to the system of m congruences of the type Pi(v)(i=1)(x(i) + s(i)) equivalent to lambda(j) (mod p) j = 1, . . . , m, modulo a prime p, with variables 1 <= x(i) <= h, i = 1, . . . , v and arbitrary integers s(j), lambda(j), j = 1, . . . , m, for a parameter h significantly smaller than p. We also mention some applications of this bound.

引用

页码：364 / 371

页数：8

共 50 条

[1] ON CONGRUENCES INVOLVING PRODUCTS OF VARIABLES FROM SHORT INTERVALS
Garaev, M. Z.
QUARTERLY JOURNAL OF MATHEMATICS, 2018, 69 (03): : 769 - 778
[2] On congruences with products of variables from short intervals and applications
Jean Bourgain
Moubariz Z. Garaev
Sergei V. Konyagin
Igor E. Shparlinski
Proceedings of the Steklov Institute of Mathematics, 2013, 280 : 61 - 90
[3] On Congruences with Products of Variables from Short Intervals and Applications
Bourgain, Jean
Garaev, Moubariz Z.
Konyagin, Sergei V.
Shparlinski, Igor E.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 280 (01) : 61 - 90
[4] Multiplicative congruences with variables from short intervals
Jean Bourgain
Moubariz Z. Garaev
Sergei V. Konyagin
Igor E. Shparlinski
Journal d'Analyse Mathématique, 2014, 124 : 117 - 147
[5] Multiplicative congruences with variables from short intervals
Bourgain, Jean
Garaev, Moubariz Z.
Konyagin, Sergei V.
Shparlinski, Igor E.
JOURNAL D ANALYSE MATHEMATIQUE, 2014, 124 : 117 - 147
[6] PRODUCTS OF INTEGERS IN SHORT INTERVALS
ERDOS, P
TURK, J
ACTA ARITHMETICA, 1984, 44 (02) : 147 - 174
[7] INFINITE SYSTEMS OF LINEAR CONGRUENCES WITH INFINITELY MANY VARIABLES
BOHR, H
FOLNER, E
MATEMATISK-FYSISKE MEDDELELSER KONGELIGE DANSKE VIDENSKABERNES SELSKAB, 1948, 24 (12): : 1 - 35
[8] On the distribution in short intervals of products of a prime and integers from a given set
Kaczorowski, J
Perelli, A
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 124 : 1 - 14
[9] Congruences with intervals and arbitrary sets
William Banks
Igor Shparlinski
Archiv der Mathematik, 2020, 114 : 527 - 539
[10] Congruences with intervals and arbitrary sets
Banks, William
Shparlinski, Igor
ARCHIV DER MATHEMATIK, 2020, 114 (05) : 527 - 539

← 1 2 3 4 5 →