D. H. J. Polymath
We prove distribution estimates for primes in arithmetic progressions to large smooth squarefree moduli, with respect to congruence classes obeying Chinese Remainder Theorem conditions, obtaining an exponent of distribution $\frac{1}{2} + \frac{7}{300}$.
D. H. J. Polymath
This paper contains 50 sections, 49 theorems, 653 equations, 1 table.
Theorem 1.1
Let $\theta=1/2+7/300$. Let $\varepsilon>0$ and $A\geq 1$ be fixed real numbers. For all primes $p$, let $a_p$ be a fixed invertible residue class modulo $p$, and for $q\geq 1$ squarefree, denote by $a_q$ the unique invertible residue class modulo $q$ such that $a_q\equiv a_p$ modulo all primes $p$ where the implied constant depends only on $A$, $\varepsilon$ and $\delta$, and in particular is in
