On the Value Distribution of Two Dirichlet L-functions

We look at the values of two Dirichlet \(L\)-functions at the Riemann zeros (or a horizontal shift of them). Off the critical line we show that for a positive proportion of these points the pairs of values of the two \(L\)-functions are linearly independent over \(\mathbb{R}\), which, in particular,...

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Bibliographic Details
Published in:arXiv.org 2015-05
Main Authors: Laaksonen, Niko, Petridis, Yiannis N
Format: Article
Language:English
Subjects:
Dirichlet problem
Online Access:Get full text
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Summary:We look at the values of two Dirichlet \(L\)-functions at the Riemann zeros (or a horizontal shift of them). Off the critical line we show that for a positive proportion of these points the pairs of values of the two \(L\)-functions are linearly independent over \(\mathbb{R}\), which, in particular, means that their arguments are different. On the critical line we show that, up to height \(T\), the values are different for \(cT\) of the Riemann zeros for some positive \(c\).
ISSN:2331-8422