Determinations of Jacobsthal sums
نویسندگان
چکیده
منابع مشابه
Sequences, Bent Functions and Jacobsthal Sums
The p-ary function f(x) mapping GF(p) to GF(p) and given by f(x) = Tr4k ( ax + bx ) with a, b ∈ GF(p) and d = p + p − p + 1 is studied with the respect to its exponential sum. In the case when either a (p+1) 6= b +1 or a = b with b 6= 0, this sum is shown to be three-valued and the values are determined. For the remaining cases, the value of the exponential sum is expressed using Jacobsthal sum...
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Explicit evaluations of several classes of trigonometric sums in closed form are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated with primitive odd characters. In this paper, we establish two general theorems involving both sines and cosines, with more attention given to cosi...
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...
متن کاملNew families of Jacobsthal and Jacobsthal-Lucas numbers
In this paper we present new families of sequences that generalize the Jacobsthal and the Jacobsthal-Lucas numbers and establish some identities. We also give a generating function for a particular case of the sequences presented. Introduction Several sequences of positive integers were and still are object of study for many researchers. Examples of these sequences are the well known Fibonacci ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1984
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1984.110.49