ADDITIVE DIOPHANTINE INEQUALITIES WITH MIXED POWERS .3.

被引：1

作者：

BRUDERN, J ^{[1
]}

机构：

[1] MATH INST,W-3400 GOTTINGEN,GERMANY

来源：

JOURNAL OF NUMBER THEORY | 1991年 / 37卷 / 02期

关键词：

D O I：

10.1016/S0022-314X(05)80037-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that if λ1, λ2...,λ7 are nonzero real numbers such that λi/λj is irrational for at least one pair i, j then the values taken by λ1x12+λ2x22+σk7=3λkxkk for integral xk are everywhere dense on the real line. A similar result is proved for λ1x13+λ2x23+...+λ6x63+λ7x74+λ8x84. A notable feature is that in contrast to earlier work it is not necessarily assumed that λ1/λ2 is irrational. © 1991 Academic Press, Inc.

引用

页码：199 / 210

页数：12

共 50 条

[1] ADDITIVE DIOPHANTINE INEQUALITIES WITH MIXED POWERS .2.
BRUDERN, J
[J]. MATHEMATIKA, 1987, 34 (68) : 131 - 140
[2] DIOPHANTINE INEQUALITIES WITH MIXED POWERS
TSANG, KM
[J]. JOURNAL OF NUMBER THEORY, 1982, 15 (02) : 149 - 163
[3] DIOPHANTINE INEQUALITIES WITH MIXED POWERS
COOK, RJ
[J]. JOURNAL OF NUMBER THEORY, 1977, 9 (01) : 142 - 152
[4] DIOPHANTINE INEQUALITIES WITH MIXED POWERS
BAKER, RC
HARMAN, G
[J]. JOURNAL OF NUMBER THEORY, 1984, 18 (01) : 69 - 85
[5] DIOPHANTINE INEQUALITIES WITH MIXED POWERS
COOK, RJ
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 57 (01) : 29 - 34
[6] DIOPHANTINE INEQUALITIES WITH MIXED POWERS .2.
COOK, RJ
[J]. JOURNAL OF NUMBER THEORY, 1979, 11 (01) : 49 - 68
[7] Additive inhomogeneous Diophantine inequalities
Freeman, DE
[J]. ACTA ARITHMETICA, 2003, 107 (03) : 209 - 244
[8] Random Diophantine inequalities of additive type
Bruedern, Joerg
Dietmann, Rainer
[J]. ADVANCES IN MATHEMATICS, 2012, 229 (06) : 3079 - 3095
[9] Diophantine approximation with mixed powers of primes
Ge, Wenxu
Liu, Huake
[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY, 2018, 14 (07) : 1903 - 1918
[10] Diophantine approximation with mixed powers of primes
Yuhui Liu
[J]. The Ramanujan Journal, 2021, 56 : 411 - 423

← 1 2 3 4 5 →