Sums of gauss, jacobi, and jacobsthal
نویسندگان
چکیده
منابع مشابه
On Gauss-Jacobi sums
In this paper, we introduce a kind of character sum which simultaneously generalizes the classical Gauss and Jacobi sums, and show that this “Gauss-Jacobi sum” also specializes to the Kloosterman sum in a particular case. Using the connection to the Kloosterman sums, we obtain in some special cases the upper bound (the “Weil bound”) of the absolute values of the Gauss-Jacobi sums. We also discu...
متن کاملUnambiguous Evaluations of Bidecic Jacobi and Jacobsthal Sums
For a class of primes p = 1 (mod 20) for which 2 is a quintic nonresidue, unambiguous evaluations of parameters of bidecic Jacobi and Jacobsthal sums (modp) are presented, in terms of the partition p = a + 5b+5c+5d, ab = d — c—cd. Similar results for sums of other orders have been obtained by E. Lehmer and by K. S. Williams. Subject classification (Amer. Math. Soc. (MOS) 1970): 10G05.
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Let p be a prime = 1 (mod 16). We obtain extensions of known congruences involving parameters of bioctic Jacobi sums (modp). These extensions are used to give an elementary proof of an important congruence of Ήasse relating parameters of quartic and octic Jacobi sums (mod p). This proof leads directly to an elementary resolution of sign ambiguities of parameters of certain quartic, octic, and b...
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In this paper we shall explore the structure of the ring of algebraic integers in any quadratic extension of the field of rational numbers Q, develop the concepts of Gauss and Jacobi sums, and apply the theory of algebraic integers and that of Gauss-Jacobi sums to solving problems involving power congruences and power sums as well as to proving the quadratic and cubic reciprocity laws. In parti...
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We study quadratic residue diierence sets, GMW diierence sets, and difference sets arising from monomial hyperovals, all of which are (2 d ?1; 2 d?1 ?1; 2 d?2 ?1) cyclic diierence sets in the multiplicative group of the nite eld F 2 d of 2 d elements, with d 2: We show that, except for a few cases with small d, these diierence sets are all pair-wise inequivalent. This is accomplished in part by...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1979
ISSN: 0022-314X
DOI: 10.1016/0022-314x(79)90008-8