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Gauss and Jacobi sums
Bruce C. Berndt,Kenneth S. Williams,Ronald J. Evans +2 more
- 01 Jan 1998
TL;DR: In this paper, Jacobi and Jacobsthal sums over finite fields have been investigated, including Jacobi Sums over Fp, Jacobi sum over Fq, Jacobit Sums and Cyclotomic Numbers over Finite Fields.
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Abstract: Gauss Sums Jacobi Sums and Cyclotomic Numbers Evaluation of Jacobi Sums Over Fp Determination of Gauss Sums Over Fp Difference Sets Jacobsthal Sums Over Fp Residuacity Reciprocity Laws Congruences for Binomial Coefficients Diagonal Equations over Finite Fields Gauss Sums over Fq Eisenstein Sums Brewer Sums A General Eisenstein Reciprocity Law Research Problems Bibliography Notation Indexes
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Citations
•Posted Content
On the $\ell$-adic valuation of certain Jacobi sums
TL;DR: In this article, the authors presented a new congruence for the Jacobi sum for the Frobenius eigenvalues of the curve, i.e., the Jacobis are Frobenians.
1
•Proceedings Article
Cyclotomic Numbers of Order 5 Over F p n
Jung-Soo Chung,Young-Sik Kim,Taehyung Lim,Jong-Seon No,Habong Chung +4 more
- 01 Jan 2005
TL;DR: In this article, the cyclotomic numbers of order 5 over an extension field Fpn were derived using the well-known results of quintic Jacobi sums over Fpn.
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Elliptic Reciprocity
TL;DR: In this article, the authors introduced the notions of elliptic pair, elliptic cycle and an elliptic list over a square free positive integer d, which are related to the notion of amicable pairs of primes and aliquot cycles introduced by Silverman and Stange.
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Some properties of the distribution of the numbers of points on elliptic curves over a finite prime field
Saiying He,James Mc Laughlin +1 more
TL;DR: In this article, the authors used elementary facts about exponential sums and known results about binary quadratic forms over finite fields to evaluate the sums of the Frobenius trace for primes in various congruence classes.
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EXPONENTIAL SUMS FOR Oð2n þ 1; qÞ AND THEIR APPLICATIONS
Dae San Kim
- 01 Jan 2001
TL;DR: For a nontrivial additive character and a multiplicative character of the finite field with q elements (q a power of an odd prime), and for each positive integer r, the exponential sums P � ððtr wÞ r Þ over w 2 SOð2n þ 1; qÞ and P � ǫ ðdet w Þ�ððr wÕ r þ over Oðn þ 2n ¼ 1; QÞ are considered in this article.
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