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On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

Let K be a totally real algebraic number field whose ring of integers R is a principal ideal domain. Let f ( x 1 , x 2 , x 3 ) be a totally definite ternary quadratic form with coefficients in R . We shall study representations of totally positive elements N R by f . We prove a quantitative formula relating the number of representations of N by different classes in the genus of f to the class number of R [ - c f N ] , where c f R is a constant depending only on f . We give an algebraic proof of a classical result of H. Maass on representations...

On n-derivations and Relations between Elements rⁿ-r for Some n

Maciej Maciejewski, Andrzej Prószyński (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We find complete sets of generating relations between the elements [r] = rⁿ - r for n = 2 l and for n = 3. One of these relations is the n-derivation property [rs] = rⁿ[s] + s[r], r,s ∈ R.

On octahedral extensions of and quadratic -curves

Julio Fernández (2003)

Journal de théorie des nombres de Bordeaux

We give a necessary condition for a surjective representation Gal ( ¯ / ) PGL 2 ( 𝔽 3 ) to arise from the 3 -torsion of a -curve. We pay a special attention to the case of quadratic -curves.

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