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On canonical subfield preserving polynomials

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Micheli G., Schipani D.

Acta Arithmetica

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2014

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tom 166

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nr 1

23-32

EN

Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.

2

Gauss Sums of Cubic Characters over $𝔽_{p^r}$, p Odd

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Schipani D., Elia M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2012

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tom 60

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nr 1

1-19

EN

An elementary approach is shown which derives the values of the Gauss sums over $𝔽_{p^r}$, 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.

3

Gauss Sums of the Cubic Character over $GF(2^m)$: an Elementary Derivation

100%

Schipani D., Elia M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2011

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tom 59

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nr 1

11-18

EN

By an elementary approach, we derive the value of the Gauss sum of a cubic character over a finite field $𝔽_{2^s}$ without using Davenport-Hasse's theorem (namely, if s is odd the Gauss sum is -1, and if s is even its value is $-(-2)^{s/2}$).

Ograniczanie wyników

2 Bulletin of the Polish Academy of Sciences. Mathematics

1 Acta Arithmetica

3 Schipani D.

2 Elia M.

1 Micheli G.

1 2014

1 2012

1 2011

On canonical subfield preserving polynomials

Gauss Sums of Cubic Characters over $𝔽_{p^r}$, p Odd

Gauss Sums of the Cubic Character over $GF(2^m)$: an Elementary Derivation