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On the distribution of Jacobi sums
Lu, Qing1,2; Zheng, Weizhe3; Zheng, Zhiyong4
2018-08-01
Source PublicationJOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
ISSN0075-4102
Volume741Pages:67-86
AbstractLet F-q be a finite field of q elements. For multiplicative characters chi(1),..., chi(m) of F-q(x), we let J (chi(1), ..., chi(m)) denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for m = 2, the normalized Jacobi sum q(-1/2) J (chi(1) , chi(2)) (chi(1), chi(2) nontrivial) is asymptotically equidistributed on the unit circle as q -> infinity, when chi(1) and chi(2) run through all nontrivial multiplicative characters of F-q(x). In this paper, we show a similar property for m >= 2. More generally, we show that the normalized Jacobi sum q(-(m-1)/2) J (chi(1), ..., chi(m)) (chi(1) ... chi(m) nontrivial) is asymptotically equidistributed on the unit circle, when chi(1), ..., chi(m) run through arbitrary sets of nontrivial multiplicative characters of F-q(x) with two of the sets being sufficiently large. The case m = 2 answers a question of Shparlinski.
DOI10.1515/crelle-2015-0087
Language英语
Funding ProjectNational Natural Science Foundation of China[11371043] ; National Natural Science Foundation of China[11321101] ; China's Recruitment Program of Global Experts ; Hua Loo-Keng Key Laboratory of Mathematics (Chinese Academy of Sciences) ; National Center for Mathematics and Interdisciplinary Sciences (Chinese Academy of Sciences) ; Program 863 grant[2013AA013702] ; Program 973 grant[2013CB834205]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000440445800003
PublisherWALTER DE GRUYTER GMBH
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30774
Collection数学所
Affiliation1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
4.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
Recommended Citation
GB/T 7714
Lu, Qing,Zheng, Weizhe,Zheng, Zhiyong. On the distribution of Jacobi sums[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,2018,741:67-86.
APA Lu, Qing,Zheng, Weizhe,&Zheng, Zhiyong.(2018).On the distribution of Jacobi sums.JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK,741,67-86.
MLA Lu, Qing,et al."On the distribution of Jacobi sums".JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK 741(2018):67-86.
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