Approximation by Shifts of Compositions of Dirichlet L -Functions with the Gram Function

Artūras Dubickas, Ramūnas Garunkštis and Antanas Laurinčikas
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Artūras Dubickas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
Ramūnas Garunkštis: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2020, vol. 8, issue 5, 1-14

Abstract: In this paper, a joint approximation of analytic functions by shifts of Dirichlet L -functions L ( s + i a 1 t τ , χ 1 ) , … , L ( s + i a r t τ , χ r ) , where a 1 , … , a r are non-zero real algebraic numbers linearly independent over the field Q and t τ is the Gram function, is considered. It is proved that the set of their shifts has a positive lower density.

Keywords: Dirichlet L -function; Gram function; joint universality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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