Explicit form for the discrete logarithm over the field ${\rm GF}(p,k)$

Gerasimos C. Meletiou

Displaying similar documents to “Explicit form for the discrete logarithm over the field $GF (p, k)$ ”

On power integral bases for certain pure number fields defined by $x^{18} - m$

Lhoussain El Fadil (2022)

Commentationes Mathematicae Universitatis Carolinae

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Let $K = ℚ (α)$ be a number field generated by a complex root $α$ of a monic irreducible polynomial $f (x) = x^{18} - m$ , $m \neq \mp 1$ , is a square free rational integer. We prove that if $m \equiv 2$ or $3 (\mod 4)$ and $m \neg \equiv \mp 1 (\mod 9)$ , then the number field $K$ is monogenic. If $m \equiv 1 (\mod 4)$ or $m \equiv 1 (\mod 9)$ , then the number field $K$ is not monogenic.

On divisibility of the class number of real octic fields of a prime conductor $p = n^{4} + 16$ by $p$

Stanislav Jakubec (1994)

Archivum Mathematicum

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The aim of this paper is to prove the following Theorem Theorem Let $K$ be an octic subfield of the field $Q (ζ_{p} + ζ_{p}^{- 1})$ and let $p = n^{4} + 16$ be prime. Then $p$ divides $h_{K}$ if and only if $p$ divides $B_{j}$ for some $j = \frac{p - 1}{8}$ , $3 \frac{p - 1}{8}$ , $5 \frac{p - 1}{8}$ , $7 \frac{p - 1}{8}$ .

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

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The information divergence of a probability measure $P$ from an exponential family $ℰ$ over a finite set is defined as infimum of the divergences of $P$ from $Q$ subject to $Q \in ℰ$ . All directional derivatives of the divergence from $ℰ$ are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for $P$ to be a maximizer of the divergence from $ℰ$ are presented, including new ones when $P$ is not projectable...

Displaying similar documents to “Explicit form for the discrete logarithm over the field GF ( p , k ) ”

On power integral bases for certain pure number fields defined by x 18 - m

On divisibility of the class number of real octic fields of a prime conductor p = n 4 + 16 by p

Optimality conditions for maximizers of the information divergence from an exponential family

Displaying similar documents to “Explicit form for the discrete logarithm over the field $GF (p, k)$ ”

On power integral bases for certain pure number fields defined by $x^{18} - m$

On divisibility of the class number of real octic fields of a prime conductor $p = n^{4} + 16$ by $p$