Zero density estimates for automorphic L-functions of \({GL_{m}}\)

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• 作者：L. Dong ; H. Liu ; D. Zhang
• 关键词：cusp form ; Maass form ; $${SL_2(\mathbb Z)}$$ S L 2 ( Z ) ; $${SL_3(\mathbb Z)}$$ S L 3 ( Z ) ; the Riemann zeta function ; automorphic L ; function ; zero density ; 11F66 ; 11M26 ; 11M41
• 刊名：Acta Mathematica Hungarica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：148
• 期：1
• 页码：191-210
• 全文大小：871 KB
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• 作者单位：L. Dong (1)
  H. Liu (2)
  D. Zhang (3)
  
  1. School of Finance, Qilu University of Technology, Jinan, Shandong, 250100, China
  2. School of Mathematics, Shandong University, Jinan, Shandong, 250100, China
  3. School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong, 250014, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Sciences
  Mathematics
  
• 出版者：Akad茅miai Kiad贸, co-published with Springer Science+Business Media B.V., Formerly Kluwer Academic
• ISSN：1588-2632

文摘

We study the zero-density estimates for automorphic L-functions \({L(s, \pi)}\) for GL _m when \({\sigma}\) is near 1. In particular, we get a range of \({\sigma}\) for which the density hypothesis holds. The proofs use a zero detecting argument, the Halász–Montgomery inequality and a bound for an integral power moment of \({L(1/2+it, \pi)}\). Key words and phrases cusp form Maass form \({SL_2(\mathbb Z)}\) \({SL_3(\mathbb Z)}\) the Riemann zeta function automorphic L-function zero density