## Well-behaved Beurling primes and integers.(English)Zbl 1154.11335

Summary: We study generalized prime systems for which both the prime and integer counting functions are asymptotically well-behaved, in the sense that they are approximately $$li(x)$$ and $$\rho x$$, respectively (where $$\rho$$ is a positive constant), with error terms of order $$O(x^{\theta_1})$$ and $$O(x^{\theta_2})$$ for some $$\theta_1, \theta_2 < 1$$. We show that it is impossible to have both $$\theta_1$$ and $$\theta_2$$ less than $$\frac{1}{2}$$.

### MSC:

 11N80 Generalized primes and integers

### Keywords:

Beurling’s generalized primes
Full Text:

### References:

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