4个素数平方及若干2的次幂和的丢番图逼近

Diophantine Approximation with 4 Squares of Primes and Powers of 2

证明了在一定条件下,不等式|λ_1p_1~2+λ_2p_2~2+λ_3p_3~2+λ_4p_4~2+μ_12^(m_1)+…+μ_s2^(m_s)+(?)|<η关于素数p1,p2,p3,p4和正整数m1,…,m_s有无穷多解,改进了之前的结果.

The authors prove that under certain conditions, the inequality ｜λ1p1^2＋λ2p2^2＋λ3p3^2＋λ4p4^2＋μ12^m1＋…＋μs2m^sa＋ ｜〈η with primes p1, p2,p3,p4 and positive integers m1,... , m8 has infinitely many solutions. This gives an improvement of the former results.