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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.
12
votes
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 …