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Riemann-type functional equations: Dirichlet polynomial approximations and a weak Gram law

Volume 204 / 2022

Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya Acta Arithmetica 204 (2022), 97-113 MSC: Primary 11M06; Secondary 30D35. DOI: 10.4064/aa210111-13-4 Published online: 20 June 2022


We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, we improve upon results of Bombieri and Friedlander on Dirichlet polynomial approximations to $L$-functions and we prove that a generalized weak Gram law for the degree-one elements of the extended Selberg class is true infinitely often.


  • Athanasios SourmelidisInstitute of Analysis and Number Theory
    TU Graz
    8010 Graz, Austria
  • Jörn SteudingDepartment of Mathematics
    University of Würzburg
    Emil Fischer-Str. 40
    97 074 Würzburg, Germany
  • Ade Irma SuriajayaFaculty of Mathematics
    Kyushu University
    744 Motooka, Nishi-ku
    Fukuoka 819-0395, Japan

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