Discrepancy bounds for distribution of automorphic L-functions

Discrepancy bounds for distribution of automorphic L-functions

In the present paper, we investigate the discrepancy D σ T ≔ sup ℛ ∣ P T log L σ + i t f ∈ ℛ − P log L σ f X ∈ ℛ ∣ , where the supremum is taken over rectangles ℛ with sides parallel to the coordinate axes. We prove that for 1 / 2 < σ < 1, we have D σ ( T ) ≪ 1 / (log T ) σ ....

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Veröffentlicht in:Lithuanian mathematical journal 2021-10, Vol.61 (4), p.550-563
Hauptverfasser: Xiao, Xuanxuan, Zhai, Shuai
Format: Artikel
Sprache:eng
Schlagworte:
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
Rectangles
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Zusammenfassung:In the present paper, we investigate the discrepancy D σ T ≔ sup ℛ ∣ P T log L σ + i t f ∈ ℛ − P log L σ f X ∈ ℛ ∣ , where the supremum is taken over rectangles ℛ with sides parallel to the coordinate axes. We prove that for 1 / 2 < σ < 1, we have D σ ( T ) ≪ 1 / (log T ) σ .
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-021-09543-8