Resolution of sign ambiguities in Jacobi and Jacobsthal sums
نویسندگان
چکیده
منابع مشابه
Resolution of Sign Ambiguities in Jacobi and Jacobsthal Sums
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 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.
متن کاملSequences, 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...
متن کاملOn 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 کاملPrimalitv Testing and Jacobi Sums
Wc present a theoretically and algorithmically simplified version of a primalitv testing algorithm that was recently invented by Adleman and Rumely. The new algorithm performs well in practice. It is the first primality test in existence that can routinely handle numbers of hundreds of decimal digits.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.81.71