Zeroes of Dirichlet $L$-functions and irregularities in the distribution of primes
Zeroes of Dirichlet $L$-functions and irregularities in the distribution of primes
Seven widely spaced regions of integers with $\pi _{4,3} (x) <\pi _{4,1} (x)$ have been discovered using conventional prime sieves. Assuming the generalized Riemann hypothesis, we modify a result of Davenport in a way suggested by the recent work of Rubinstein and Sarnak to prove a theorem which makes it …