On Second Moment of Selberg Zeta-Function for σ=1

On Second Moment of Selberg Zeta-Function for σ=1

Let Z ( s ) be the Selberg zeta-function for the modular group. We consider the existence of the second moments of Z ( s ) and of its reciprocal on σ = 1 . The existence of such moments is related to the properties of certain Beurling natural numbers. Here the behavior of the counting function and t...

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Veröffentlicht in:Resultate der Mathematik 2021-12, Vol.76 (4), Article 184
Hauptverfasser: Drungilas, Paulius, Garunkštis, Ramūnas, Novikas, Aivaras
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
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Zusammenfassung:Let Z ( s ) be the Selberg zeta-function for the modular group. We consider the existence of the second moments of Z ( s ) and of its reciprocal on σ = 1 . The existence of such moments is related to the properties of certain Beurling natural numbers. Here the behavior of the counting function and the distribution of minimal gaps between these Beurling natural numbers are important. We also obtain unconditional upper bounds for these moments.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-021-01492-5