Open Access
March 2018 On the value distribution of two Dirichlet $\boldsymbol L$-functions
Niko Laaksonen, Yiannis N. Petridis
Funct. Approx. Comment. Math. 58(1): 43-68 (March 2018). DOI: 10.7169/facm/1640


Let $\rho$ denote the non-trivial zeros of the Riemann zeta function. We study the relative value distribution of $L(\rho+\sigma,\chi_{1})$ and $L(\rho+\sigma,\chi_{2})$, where $\sigma\in[0,1/2)$ is fixed and $\chi_{1}$, $\chi_{2}$ are two fixed Dirichlet characters to distinct prime moduli. For $\sigma>0$ we prove that a positive proportion of these pairs of values are linearly independent over $\mathbb{R}$, which implies that the arguments of the values are different. For $\sigma=0$ we show that, up to height $T$, the values are different for $cT$ of the Riemann zeros for some positive constant $c$.


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Niko Laaksonen. Yiannis N. Petridis. "On the value distribution of two Dirichlet $\boldsymbol L$-functions." Funct. Approx. Comment. Math. 58 (1) 43 - 68, March 2018.


Published: March 2018
First available in Project Euclid: 5 May 2017

zbMATH: 06924915
MathSciNet: MR3780033
Digital Object Identifier: 10.7169/facm/1640

Primary: 11M06
Secondary: 11M26

Keywords: Dirichlet $L$-function , value-distribution

Rights: Copyright © 2018 Adam Mickiewicz University

Vol.58 • No. 1 • March 2018
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