Moscow Journal of Combinatorics and Number Theory
- Mosc. J. Comb. Number Theory
- Volume 8, Number 3 (2019), 229-245.
On the distribution of values of Hardy's $Z$-functions in short intervals, II: The $q$-aspect
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.
Mosc. J. Comb. Number Theory, Volume 8, Number 3 (2019), 229-245.
Received: 10 November 2018
Revised: 7 May 2019
Accepted: 31 May 2019
First available in Project Euclid: 13 August 2019
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Mawia, Ramdin. On the distribution of values of Hardy's $Z$-functions in short intervals, II: The $q$-aspect. Mosc. J. Comb. Number Theory 8 (2019), no. 3, 229--245. doi:10.2140/moscow.2019.8.229. https://projecteuclid.org/euclid.moscow/1565661748