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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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Bilinear forms in Weyl sums for modular square roots and applications
TL;DR: In this article, a lower bound for the number of rational primes that split in the imaginary quadratic field was established for any fixed ε > 0. This lower bound was improved by the work of Pollack and Benli-Pollack, who proved an estimate for a bilinear form involving Weyl sums for modular square roots.
The Spherical Kakeya Problem in Finite Fields
TL;DR: In this paper, subsets of the $n$-dimensional vector space over the finite field for odd $q, which contain either a sphere for each radius or a sphere in each first coordinate of the vector space, are studied.
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Fourier coefficients of Siegel cusp forms of degree 2 in the Atkin--Lehner type newspace
TL;DR: In this paper, it was shown that the Atkin-Lehner type Siegel newspace of degree 2 is determined by fundamental Fourier coefficients up to a divisor of degree 1.
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Zeta function factorisation, Dwork hypersurfaces, hypergeometric hypersurfaces
TL;DR: In this article, it was shown that the zeta function of the projective variety over a finite field has an explicit decomposition in factors coming from affine varieties of odd dimension, which are of hypergeometric type.
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On a generalization of Jacobi sums
TL;DR: In this article, the authors proved an estimate for multi-variable multiplicative character sums over affine subspaces of A^n_k, which generalize the well known estimates for both classical Jacobi sums and one-variable polynomial multiplicative characters sums.
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