Geodesic
Dirichlet Series with Periodic Coefficients and Their Value-Distribution near the Critical Line
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 248-274

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The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series $L(s;f)$ and their analytic continuation in the neighbourhood of the critical line (which is the axis of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number $a\neq 0$, we find for an even or odd periodic $f$ the number of $a$-points of the $\Delta $-factor of the functional equation, prove the existence of the mean of the values of $L(s;f)$ taken at these points, show that the ordinates of these $a$-points are uniformly distributed modulo one and apply this to show a discrete universality theorem.
Keywords: Dirichlet L-functions, Dirichlet series, periodic coefficients, critical line, uniform distribution, universality, Julia line. 
@article{TM_2021_314_a10,
     author = {Athanasios Sourmelidis and J\"orn Steuding and Ade Irma Suriajaya},
     title = {Dirichlet {Series} with {Periodic} {Coefficients} and {Their} {Value-Distribution} near the {Critical} {Line}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {248--274},
     publisher = {mathdoc},
     volume = {314},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_314_a10/}
}
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Athanasios Sourmelidis; Jörn Steuding; Ade Irma Suriajaya. Dirichlet Series with Periodic Coefficients and Their Value-Distribution near the Critical Line. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and Combinatorial Number Theory, Tome 314 (2021), pp. 248-274. http://geodesic.mathdoc.fr/item/TM_2021_314_a10/