Theorems on Brewer and Jacobsthal sums. II.
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...
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 کاملResolution 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 کاملLimit Theorems for Theta Sums
For almost all values of x 2 R, the classical theta sum S N (x) = N ?1=2 N X n=1 e 2i n 2 x exhibits an extremely irregular behaviour, as N tends to innnity. This limit is investigated by exploiting a connection to the ergodic properties of ows on the unit tangent bundle of a surface of constant negative curvature.
متن کاملInverse Theorems for Subset Sums
Let A be a nite set of integers. For h 1, let S h (A) denote the set of all sums of h distinct elements of A. Let S(A) denote the set of all nonempty sums of distinct elements of A. The direct problem for subset sums is to nd lower bounds for jS h (A)j and jS(A)j in terms of jAj. The inverse problem for subset sums is to determine the structure of the extremal sets A of integers for which jS h ...
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: Michigan Mathematical Journal
سال: 1965
ISSN: 0026-2285
DOI: 10.1307/mmj/1028999246