New Zero-Density Results for Automorphic L -Functions of GL ( n )

Wenjing Ding, Huafeng Liu and Deyu Zhang
Additional contact information
Wenjing Ding: School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
Huafeng Liu: School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
Deyu Zhang: School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Mathematics, 2021, vol. 9, issue 17, 1-13

Abstract: Let L ( s , ? ) be an automorphic L -function of G L ( n ) , where ? is an automorphic representation of group G L ( n ) over rational number field Q . In this paper, we study the zero-density estimates for L ( s , ? ) . Define N ? ( ? , T 1 , T 2 ) = ? { ? = ? + i ? : L ( ? , ? ) = 0, ? < ? < 1 , T 1 ? ? ? T 2 }, where 0 ? ? < 1 and T 1 < T 2 . We first establish an upper bound for N ? ( ? , T , 2 T ) when ? is close to 1. Then we restrict the imaginary part ? into a narrow strip [ T , T + T ? ] with 0 < ? ? 1 and prove some new zero-density results on N ? ( ? , T , T + T ? ) under specific conditions, which improves previous results when ? near 3 4 and 1, respectively. The proofs rely on the zero detecting method and the Halász-Montgomery method.

Keywords: zero density; automorphic L-function; automorphic representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/17/2061/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/17/2061/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:17:p:2061-:d:622765

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().