A Chebyshev type upper estimate for prime elements in additive arithmetic semigroups

作者：Zhang WB^*

来源：Monatshefte fur Mathematik, 2000, 129(3): 227-260.

DOI：10.1007/s006050050073

• Chebyshev-type upper estimate
• additive arithmetic semigroup
• approximate convolution inverse

Let G(n) and Lambda(n) be two sequences of nonnegative numbers which satisfy G(0) = 1 and an additive convolution equation (Lambda (*) G)(n) = nG(n), n = 0, 1,2,.... A Chebyshev-type upper estimate for prime elements in an additive arithmetic semigroup is essentially a tauberian theorem on Lambda(n) and G(n). Suppose
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with real constants 0 less than or equal to rho(1) < (...) < rho(r), rho(r) greater than or equal to 1, A(1),...,A(r), A(r) > 0. The theorem proved here stales that Lambda(n) much less than q(n) and that Sigma(m=1)(,)(n) Lambda(m)q(-m) = rho(r)n + R(n) + O(1) holds with an explicit function R(n) of order < 1 in n. This theorem is sharp. It has several applications.

• 出版日期2000
• 单位华南理工大学