All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 187

Showing per page

On the arithmetic of cross-ratios and generalised Mertens’ formulas

Jouni Parkkonen, Frédéric Paulin (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We develop the relation between hyperbolic geometry and arithmetic equidistribution problems that arises from the action of arithmetic groups on real hyperbolic spaces, especially in dimension ≤ 5 . We prove generalisations of Mertens’ formula for quadratic imaginary number fields and definite quaternion algebras over ℚ , counting results of quadratic irrationals with respect to two different natural complexities, and counting results of representations of (algebraic) integers by binary quadratic, Hermitian...

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 closed subfields of [...] Q ¯   p Q ¯ ˜ p

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

Open Mathematics

Let p be a prime number, and let [...] Q¯ p 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 Q ¯ ˜ 𝐩 , the completion of Q with respect w, i.e. the spectral extension of the p-adic valuation vp on Q.

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 computation of quadratic 2 -class groups

Wieb Bosma, Peter Stevenhagen (1996)

Journal de théorie des nombres de Bordeaux

We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D ≡ 0 , 1 mod 4 and the factorization of D , computes the structure of the 2 -Sylow subgroup of the class group of the quadratic order of discriminant D in random polynomial time in log D .

On the finiteness of Pythagoras numbers of real meromorphic functions

Francesca Acquistapace, Fabrizio Broglia, José F. Fernando, Jesús M. Ruiz (2010)

Bulletin de la Société Mathématique de France

We consider the 17th Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real global analytic function to be a sum of squares of global real meromorphic functions. We deduce that an affirmative solution to the 17th Hilbert Problem for global real analytic functions implies the finiteness of the Pythagoras number of the field of global real meromorphic functions, hence that of the field of real...

Currently displaying 81 – 100 of 187