That being said, it does require Siegel-Walfisz theorem (an asymptotic
for the sum of log p for primes p = a (mod n)).

Thank you Savely!

I think a lot of Mario's material from the Prime Number Theorem can be
used as a basis, including von Mangoldt's and Euler's phi functions.
Mario also mentioned the methods to compute the integrals might be similar.

What about Nathanson, Melvyn B. (1996). /Additive number theory. The
classical bases/ (ISBN 0-387-94656-X): could we use this textbook as a
reference?

BR,
_
Thierry

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