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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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Roth's theorem for primes in a given arithmetic progression to a large modulus

Let $\mathbb{P}_{a, q}$ denote the set of primes congruent to $a$ modulo $q$. Are there any estimates for the number of $3$-Arithmetic Progressions in the set $\mathbb{P}_{a, q}\cap [1, X]$, where $(a …
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