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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Springer Berlin Heidelberg

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DOI

10.1002/ncr.4110400811

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1869-1862

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Cyclotomic problem Gauss sums and Legendre curve

Authors: LingLi Xia Jing Yang
Publish Date: 2013/06/05
Volume: 56, Issue: 7, Pages: 1485-1508
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Abstract

In this paper explicit determination of the cyclotomic numbers of order l and 2l for odd prime l ≡ 3 mod 4 over finite field mathbbF q in the index 2 case are obtained utilizing the explicit formulas on the corresponding Gauss sums The main results in this paper are related with the number of rational points of certain elliptic curve called “Legendre curve” and the properties and value distribution of such number are also presented

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