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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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Upper bounds for the sum of primes up to $n$

There definitely are earlier references than our book. An asymptotic formula for $\sum_{p \leq x} p^a$ is in T. Salát and S. Znám, On the sums of the prime powers, Acta Fac. Rer. Nat. Univ. Com. M …
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