ON THE REPRESENTATION OF LARGE INTEGERS BY INTEGRAL TERNARY POSITIVE-DEFINITE QUADRATIC-FORMS

被引：0

作者：

MOROZ, BZ ^{[1
]}

机构：

[1] MAX PLANCK INST MATH,W-5300 BONN 3,GERMANY

来源：

ASTERISQUE | 1992年 / 209期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a conjecture of Heath-Brown to the extent that every sufficiently large integer congruent to 7 modulo 8 is represented by the quadratic form x2 + y2 - p3z2, where p is a rational prime congruent to 5 modulo 8 (in particular, by the form x2 + y2 + 125z2), and discuss some related results.

引用

页码：275 / 278

页数：4

共 50 条

[1] ON THE REPRESENTATION OF INTEGERS WITH LARGE SQUARE FACTORS BY POSITIVE DEFINITE TERNARY QUADRATIC-FORMS
EARNEST, AG
[J]. MATHEMATIKA, 1984, 31 (62) : 252 - 257
[2] THE REPRESENTATION OF A PAIR OF INTEGERS BY A PAIR OF POSITIVE-DEFINITE BINARY QUADRATIC-FORMS
HARDY, K
KAPLAN, P
WILLIAMS, KS
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 105 (04) : 847 - 855
[3] THE REPRESENTATION OF BINARY QUADRATIC-FORMS BY POSITIVE-DEFINITE QUATERNARY QUADRATIC-FORMS
EARNEST, AG
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 345 (02) : 853 - 863
[4] THE MINIMUM AND THE PRIMITIVE REPRESENTATION OF POSITIVE-DEFINITE QUADRATIC-FORMS
KITAOKA, Y
[J]. NAGOYA MATHEMATICAL JOURNAL, 1994, 133 : 127 - 153
[5] REPRESENTATION BY DEFINITE TERNARY QUADRATIC-FORMS
SCHULZEPILLOT, R
[J]. JOURNAL OF NUMBER THEORY, 1982, 14 (02) : 237 - 250
[6] ON THE DISTRIBUTION OF POSITIVE-DEFINITE GAUSSIAN QUADRATIC-FORMS
TZIRITAS, GG
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1987, 33 (06) : 895 - 906
[7] Representation of integers by special positive definite integral quadratic forms
Kohnen, Winfried
[J]. QUADRATIC FORMS - ALGEBRA, ARITHMETIC, AND GEOMETRY, 2009, 493 : 243 - 247
[8] Exceptional integers for genera of integral ternary positive definite quadratic forms
Schulze-Pillot, R
[J]. DUKE MATHEMATICAL JOURNAL, 2000, 102 (02) : 351 - 357
[9] A NOTE ON REPRESENTATION OF POSITIVE DEFINITE BINARY QUADRATIC-FORMS BY POSITIVE DEFINITE QUADRATIC-FORMS IN 6 VARIABLES
KITAOKA, Y
[J]. ACTA ARITHMETICA, 1990, 54 (04) : 317 - 322
[10] LEVELS OF POSITIVE DEFINITE TERNARY QUADRATIC-FORMS
LEHMAN, JL
[J]. MATHEMATICS OF COMPUTATION, 1992, 58 (197) : 399 - &

← 1 2 3 4 5 →