Small first zeros of \(L\) -functions

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• 作者：Damien Bernard (1)
  
  1. Laboratoire de Math茅matiques ; Universit茅 Blaise Pascal ; Campus des C茅zeaux ; BP 80026 ; 63171 ; Aubi猫re Cedex ; France
  
• 关键词：$$L$$ L ; function ; Density theorem ; Random matrix theory ; Smallest zero ; Differential equation with temporal shifts ; 11M41 ; 11M50 ; 11F67
• 刊名：Monatshefte für Mathematik
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：176
• 期：3
• 页码：359-411
• 全文大小：673 KB
• 参考文献：1. Brezis, H.: Functional Analysis. Sobolev Spaces and Partial Differential Equations. Universitext. Springer, New York (2011)
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  13. Ricotta, G., Royer, E.: Lower order terms for the one-level densities of symmetric power \(L\) -functions in the level aspect. Acta Arith. 141(2), 153鈥?70 (2010) CrossRef
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• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081

文摘

From a family of \(L\) -functions with unitary symmetry, Hughes and Rudnick obtained results on the height of its lowest zero. We extend their results to other families of \(L\) -functions according to the type of symmetry coming from statistics for low-lying zeros.