Saving the logarithmic factor in the error term estimates of some congruence problems

被引：3

作者：

Cilleruelo, Javier ^{[1
]}

Zumalacarregui, Ana ^{[2
]}

机构：

[1] Univ Autonoma Madrid, Inst Ciencias Matemat, Dept Matemat, CSIC UAM UC3M UCM, E-28049 Madrid, Spain

[2] Univ New South Wales, Dept Pure Math, Sydney, NSW 2052, Australia

来源：

MATHEMATISCHE ZEITSCHRIFT | 2017年 / 286卷 / 1-2期

基金：

澳大利亚研究理事会;

关键词：

EXPONENTIAL-SUMS;

D O I：

10.1007/s00209-016-1771-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Combining previous ideas from Garaev and the first author, we prove a general theorem to estimate the number of elements of a subset A of an abelian group lying in a k-dimensional box. In many cases, this approach allow us to improve, by a logarithm factor, the range where it is possible to obtain an asymptotic estimate for the number of solutions of a given congruence.

引用

页码：545 / 558

页数：14

共 12 条

[1] ON EXPONENTIAL SUMS IN FINITE FIELDS [J].

BOMBIERI, E .

AMERICAN JOURNAL OF MATHEMATICS, 1966, 88 (01) :71-&

[2] Combinatorial problems in finite fields and Sidon sets [J].

Cilleruelo, Javier .

COMBINATORICA, 2012, 32 (05) :497-511

[3]

DELIGNE P., 1977, Lecture Notes in Math., V569, DOI [10.1007/BFb0091526, DOI 10.1007/BFB0091526, DOI 10.1007/BFB0091523]

[4]

Fouvry E, 2001, J REINE ANGEW MATH, V540, P115

[5] On the logarithmic factor in error term estimates in certain additive congruence problems [J].

Garaev, M. Z. .

ACTA ARITHMETICA, 2006, 124 (01) :27-39

[6]

Heath-Brown D.R., 2000, Nieuw Arch. Wiskd. (5), V1, P380

[7]

HOOLEY C., 1982, London Mathematical Society, Lecture Notes Series, V56, P92

[8]

Iwaniec H., 2004, Colloquium Publications

[9]

Lang S., 1954, Amer. J. Math., V76, P819

[10] ON THE DISCRIMINANT OF A HYPERELLIPTIC CURVE [J].

LOCKHART, P .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 342 (02) :729-752

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