Diophantine Approximation by Cubes of Primes and an Almost Prime II
نویسندگان
چکیده
Let λ1, . . . , λ4 be non-zero with λ1/λ2 irrational and negative, and let S be the set of values attained by the form λ1x 3 1 + · · · + λ4x4 when x1 has at most 3 prime divisors and the remaining variables are prime. We prove that most real numbers are close to an element of S.
منابع مشابه
Diophantine Approximation by Cubes of Primes and an Almost Prime
Let λ1, . . . , λs be non-zero with λ1/λ2 irrational and let S be the set of values attained by the form λ1x 3 1 + · · ·+ λsxs when x1 has at most 6 prime divisors and the remaining variables are prime. In the case s = 4, we establish that most real numbers are “close” to an element of S. We then prove that if s = 8, S is dense on the real line.
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