A Diophantine problem with a prime and three squares of primes

作者：Languasco Alessandro^*; Zaccagnini Alessandro

来源：Journal of Number Theory, 2012, 132(12): 3016-3028.

DOI：10.1016/j.jnt.2012.06.015

• Goldbach-type theorems
• Hardy-Littlewood method
• Diophantine inequalities

We prove that if lambda(1), lambda(2), lambda(3) and lambda(4) are non-zero real numbers not all of the same sign, lambda(1)/lambda(2) is irrational, and pi is any real number then, for any epsilon %26gt; 0, the inequality vertical bar lambda(1)p(1) + lambda(2)p(2)(2) + lambda(3)p(3)(2) + lambda(4)p(4)(2) + pi vertical bar %26lt;= (max(j) p(j))(-1/18+epsilon) has infinitely many solutions in prime variables p(1), ..., p(4).

• 出版日期2012-12