The quadratic Waring-Goldbach problem

被引：18

作者：

Liu, JY

Wooley, TD

Yu, G

机构：

[1] Leconte Coll, Coll Sci & Math, Dept Math, Columbia, SC 29208 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[3] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2004年 / 107卷 / 02期

基金：

美国国家科学基金会;

关键词：

Waring-Goldbach problem; Hardy-Littlewood method; Dirichlet L-functions;

D O I：

10.1016/j.jnt.2004.04.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is conjectured that Lagrange's theorem of four squares is true for prime variables, i.e. all positive integers n with n equivalent to 4 (mod 24) are the sum of four squares of primes. In this paper, the size for the exceptional set in the above conjecture is reduced to O(N3/8+epsilon). (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：298 / 321

页数：24

共 20 条

[1]

BRUDERN J, 1994, J REINE ANGEW MATH, V454, P59

[2]

Davenport H., 1980, MULTIPLICATIVE NUMBE

[3] LARGE SIEVE DENSITY ESTIMATE NEAR SIGMA=1 [J].

GALLAGHER, PX .

INVENTIONES MATHEMATICAE, 1970, 11 (04) :329-+

[4]

GHOSH A, 1981, P LOND MATH SOC, V42, P252

[5]

Greaves G., 1976, ACTA ARITH, V29, P257

[6]

Heath-Brown DR, 2003, J REINE ANGEW MATH, V558, P159

[7] PRIME-NUMBERS IN SHORT INTERVALS AND A GENERALIZED VAUGHAN IDENTITY [J].

HEATHBROWN, DR .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1982, 34 (06) :1365-1377

[8]

Hua LK., 1938, Q J MATH OXFORD, V9, P68, DOI [10.1093/qmath/os-9.1.68, DOI 10.1093/QMATH/OS-9.1.68]

[9]

Huxley M N., 1974, Acta Arithmetica, V26, P435, DOI DOI 10.4064/AA-26-4-435-444

[10] LINNIKS CONSTANT [J].

JUTILA, M .

MATHEMATICA SCANDINAVICA, 1977, 41 (01) :45-62

← 1 2 →