The large sieve for square moduli under Hooley's hypothesis $R^{\ast }$

Stephan Baier

Let $S(Q,M,N,(a_n)):={\sum }_{q\le Q}{\sum }_{(a,q)=1}|{\sum }_{M<n\le M+N}{a}_{n}e(an/q^2){|}^2$ be Zhao's large sieve sum with square moduli. At the critical point $N=Q^3$ the best known uncond…