We continue our investigations regarding the distribution of positive and negative values of Hardy’s -functions in the interval when the conductor and both tend to infinity. We show that for , , with , satisfying , the Lebesgue measure of the set of values of for which is as , where denotes the number of distinct prime factors of the conductor of the character , and is the usual Euler totient. This improves upon our earlier result. We also include a corrigendum for the first part of this article.
"On the distribution of values of Hardy's $Z$-functions in short intervals, II: The $q$-aspect." Mosc. J. Comb. Number Theory 8 (3) 229 - 245, 2019. https://doi.org/10.2140/moscow.2019.8.229