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

Author

Listed:
  • Artūras Dubickas

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Ramūnas Garunkštis

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Antanas Laurinčikas

    (Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Artūras Dubickas & Ramūnas Garunkštis & Antanas Laurinčikas, 2020. "Approximation by Shifts of Compositions of Dirichlet L -Functions with the Gram Function," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:751-:d:355760
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