On the value distribution of two Dirichlet L-functions over sums of two zeros of the Riemann zeta-function
Article Sidebar
Main Article Content
Abstract
Let and
denote the non-trivial zeros of the Riemann zeta-function
with
and
. Under the assumption of the Riemann Hypothesis, we show that for a positive proportion of
, the values of the Dirichlet
-function
and
associated with the primitive characters
and
to different prime moduli are linearly independent over
.
Article Details
References
Fujii A. An additive theory of the zeros of the Riemann zeta function. Rikkyo Daigaku sugaku zasshi. 1996. 45 : 49-116.
Fujii A. On the zeros of Dirichlet L-functions. V. Acta Arith. 1976. 28: 395-403.
Laaksonen N. and Petridis Y. N. On the value distribution of two Dirichlet L-functions. Functiones et Approximatio Commentarii Mathematici. 2018. 58 : 43-68.
Lavrik A.F. An approximate functional equation for Dirichlet L-functions. Trans. Moscow Math. Soc. 1859. 18 : 101-115.
Riemann B. Über die Anzahl der Primzahlen unter einer gegebenen Grösse. Ges. Math. Werke und Wissenschaftlicher Nachlaß. 1968. 2 : 145-155.
Steuding J. Value-distribution of L-functions. Springer, Berlin. 2007.
Titchmarsh E.C., Titchmarsh E.C.T. and Heath-Brown D.R. The theory of the Riemann zeta- function. Oxford University Press. 1986.