Hooley's delta function

Hooley's delta function, often denoted as \( \Delta(s) \), is a mathematical tool used in number theory, particularly in the context of the Generalized Riemann Hypothesis and the distribution of prime numbers. It was introduced by C. Hooley in his work related to the study of integers represented by quadratic forms and sieve methods. The function is defined in terms of the values of L-functions, specifically for certain Dirichlet series associated with characters.