Chebyshev estimates for Beurling generalized prime numbers. I

摘要

We provide new sufficient conditions for Chebyshev estimates for Beurling generalized primes. It is shown that if the counting function N of a generalized number system satisfies the L ~1-condition∫ _1 ~∞|N(x)-ax/x|dx/x<∞ and N(x)=ax+o(x/logx), for some a>0, then 0