Translator Disclaimer
2019 On the distribution of values of Hardy's $Z$-functions in short intervals, II: The $q$-aspect
Ramdin Mawia
Mosc. J. Comb. Number Theory 8(3): 229-245 (2019). DOI: 10.2140/moscow.2019.8.229

Abstract

We continue our investigations regarding the distribution of positive and negative values of Hardy’s Z-functions Z(t,χ) in the interval [T,T+H] when the conductor q and T both tend to infinity. We show that for qTη, H=Tϑ, with ϑ>0, η>0 satisfying 12+12η<ϑ1, the Lebesgue measure of the set of values of t[T,T+H] for which Z(t,χ)>0 is (φ(q)24ω(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.

Citation

Download Citation

Ramdin Mawia. "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

Information

Received: 10 November 2018; Revised: 7 May 2019; Accepted: 31 May 2019; Published: 2019
First available in Project Euclid: 13 August 2019

zbMATH: 07095942
MathSciNet: MR3990806
Digital Object Identifier: 10.2140/moscow.2019.8.229

Subjects:
Primary: 11M06, 11M26

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.8 • No. 3 • 2019
MSP
Back to Top