Irregularities in the distribution of primes in arithmetic progressions. II (Q762545)

With the same finite Riemann-Piltz assumption as in part I (see the preceding review), the authors extend those results by obtaining lower bounds for various definite integrals of \(| \Delta_ i(x)|\), \(i=1,2,3,4\), where the meaning for \(i=2,4\) is given in the review of part I. \(\Delta_ 1(x)=\sum_{p\leq x, p\equiv \ell_ 1 (q)}1-\sum_{p\leq x, p\equiv \ell_ 2 (q)}1\) and \(\Delta_ 3(x)\) is the same difference with summands log p.