On the distribution of values of Hardy’s Z-functions in short intervals II: The q-aspect
Article Type
Research Article
Publication Title
Moscow Journal of Combinatorics and Number Theory
Abstract
We continue our investigations regarding the distribution of positive and negative values of Hardy’s Zfunctions Z(t, χ) in the interval [T, T + H] when the conductor q and T both tend to infinity. We show that for q ≤ Tη, H = Tϑ, with ϑ > 0, η > 0 satisfying 1\2+ 1\2 η < ϑ ≤ 1, the Lebesgue measure of the set of 2 values of t ϵ [T, T + H] for which Z(t, χ) > 0 is >> (ϕ(q)2/4ω(q)q2)H as T → ∞, where ω(q) denotes the number of distinct prime factors of the conductor q of the character χ, and ϕ is the usual Euler totient. This improves upon our earlier result. We also include a corrigendum for the first part of this article.
First Page
229
Last Page
245
DOI
10.2140/moscow.2019.8.229
Publication Date
1-1-2019
Recommended Citation
Mawia, Ramdin, "On the distribution of values of Hardy’s Z-functions in short intervals II: The q-aspect" (2019). Journal Articles. 994.
https://digitalcommons.isical.ac.in/journal-articles/994