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On the classification of 3-dimensional non-associative division algebras over $p$ -adic fields

Abdulaziz Deajim, David Grant (2011)

Journal de Théorie des Nombres de Bordeaux

Let $p$ be a prime and $K$ a $p$ -adic field (a finite extension of the field of $p$ -adic numbers $ℚ_{p}$ ). We employ the main results in [12] and the arithmetic of elliptic curves over $K$ to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over $K$ to the classification of ternary cubic forms $H$ over $K$ (up to equivalence) with no non-trivial zeros over $K$ . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...

On the Classification of Hermitian Forms.

C.T.C. Wall (1972)

Inventiones mathematicae

On the classification of hermitian forms. I. Rings of algebraic integers

C. T. C. Wall (1970)

Compositio Mathematica

On the Classification of Hermitian Forms. III. Complete Semilocal Rings.

C.T.C. Wall (1973)

Inventiones mathematicae

On the classification of Hilbert Modular threefolds.

H.G. Grundman (1991)

Manuscripta mathematica

On the classification of quadratic forms over semi local rings

Ricardo Baeza (1979)

Mémoires de la Société Mathématique de France

On the class-number of the maximal real subfield of a cyclotomic field.

Itaru Yamaguchi (1975)

Journal für die reine und angewandte Mathematik

On the closed subfields of [...] Q ¯ p ${\tilde{\bar{Q}}}_{p}$

Sever Achimescu, Victor Alexandru, Corneliu Stelian Andronescu (2016)

Open Mathematics

Let p be a prime number, and let [...] Q¯ p ${\tilde{\bar{Q}}}_{𝐩}$ be the completion of Q with respect to the pseudovaluation w which extends the p-adic valuation vp. In this paper our goal is to give a characterization of closed subfields of [...] Q¯ p ${\tilde{\bar{Q}}}_{𝐩}$ , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

On the closedness of approximation spectra

Jouni Parkkonen, Frédéric Paulin (2009)

Journal de Théorie des Nombres de Bordeaux

Generalizing Cusick’s theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant [Mau].

On the coefficients cn in the expansion ... .

S. Chowla, M. Cowles (1977)

Journal für die reine und angewandte Mathematik

On the coefficients of Drinfeld modular forms.

Ernst-Ulrich Gekeler (1988)

Inventiones mathematicae

On the coefficients of the $2^{n}$ -th transformation polynomial for j(ω)

Kurt Mahler (1972)

Acta Arithmetica

On the coefficients of the asymptotic expansion of $n!$ .

Nemes, Gergő (2010)

Journal of Integer Sequences [electronic only]

On the coefficients of the cyclotomic polynomial

Erdös, P. (1949)

Portugaliae mathematica

On the coefficients of the Taylor expansion of the Dirichlet L-function at s = 1

Hideaki Ishikawa (2001)

Acta Arithmetica

On the Cohomological Characterization of Real Free Pro-2-Group.

Antonio José Engler (1995)

Manuscripta mathematica

On the cohomology of biquadratic extensions.

Bruno Kahn (1994)

Commentarii mathematici Helvetici

On the cokernel of the Witt decomposition map

Gabriele Nebe (2000)

Journal de théorie des nombres de Bordeaux

Let $R$ be a Dedekind domain with field of fractions $K$ and $G$ a finite group. We show that, if $R$ is a ring of $p$ -adic integers, then the Witt decomposition map $δ$ between the Grothendieck-Witt group of bilinear $K G$ -modules and the one of finite bilinear $R G$ -modules is surjective. For number fields $K, δ$ is also surjective, if $G$ is a nilpotent group of odd order, but there are counterexamples for groups of even order.

On the Collatz conjecture

Sebastian Hebda (2013)

Colloquium Mathematicae

We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.

On the collineation group of a normal projective abelian variety

Federico Gaeta (1975)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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