Orthant spanning simplexes with minimal volume.
A note on Fibonacci matrices of even degree.
Integration of the exponential function of a complex quadratic form.
Gauss Sums of Cubic Characters over , p Odd
An elementary approach is shown which derives the values of the Gauss sums over , p odd, of a cubic character. New links between Gauss sums over different field extensions are shown in terms of factorizations of the Gauss sums themselves, which are then revisited in terms of prime ideal decompositions. Interestingly, one of these results gives a representation of primes p of the form 6k+1 by a binary quadratic form in integers of a subfield of the cyclotomic field of the pth roots of unity.
Gauss Sums of the Cubic Character over : an Elementary Derivation
By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field without using Davenport-Hasse’s theorem (namely, if s is odd the Gauss sum is -1, and if s is even its value is ).
Improvements on the Cantor-Zassenhaus factorization algorithm
The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed for factoring....
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