科研之友
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摘要
Let d a (c) 3/4 3 be an integer, and set r = 2 (d-1) + 1 for 3 a (c) 1/2 d a (c) 1/2 4, for 5 a (c) 1/2 d a (c) 1/2 6, r = d (2)+d+1 for 7 a (c) 1/2 d a (c) 1/2 8, and r = d (2)+d+2 for d a (c) 3/4 9, respectively. Suppose that I broken vertical bar (i) (x, y) a a"<currency>[x, y] (1 a (c) 1/2 i a (c) 1/2 r) are homogeneous and nondegenerate binary forms of degree d. Suppose further that lambda(1), lambda(2),..., lambda (r) are nonzero real numbers with lambda(1)/lambda(2) irrational, and lambda I-1 broken vertical bar(1)(x (1), y (1)) + lambda I-2 broken vertical bar(2)(x (2), y (2)) + center dot center dot center dot + lambda (r) I broken vertical bar (r) (x (r) , y (r) ) is indefinite. Then for any given real eta and sigma with 0 < sigma < 2(2-d) , it is proved that the inequality has infinitely many solutions in integers x (1), x (2),..., x (r) , y (1), y (2),..., y (r) . This result constitutes an improvement upon that of B. Q. Xue.
- 出版日期2017-12
- 单位西安工程大学
