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The Frobenius traces distribution for modular Abelian surfaces
(2014-02)
Article.
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Article.
Accés restringit per política de l'editorial
We prove that there exist at least 15 pairs of measures for which the two normalized Frobenius traces on modular Abelian surfaces are equidistributed. Under an assumption about stochastic independence, we prove that there ...
Newton polygons of higher order in algebraic number theory
(2012-01-10)
Article.
Accés obert
Article.
Accés obert
We develop a theory of arithmetic Newton polygons of higher
order, that provides the factorization of a separable polynomial over a p-adic
eld, together with relevant arithmetic information about the elds generated
by ...
Cropping Euler factors of modular L-functions
(2013-09)
Article.
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Article.
Accés obert
According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
On the Torelli problem and Jacobian Nullwerte in genus three
(2008)
Article.
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Article.
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We give a closed formula for recovering a non-hyperelliptic genus three curve from its period matrix, and derive some identities between Jacobian Nullwerte in dimension three.
The automorphism group of the non-split Cartan modular curve of level 11
(2014-11-01)
Article.
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Article.
Accés restringit per política de l'editorial
We derive equations for the modular curve X-ns(11) associated to a non-split Cartan subgroup of GL(2)(F-11). This allows us to compute the automorphism group of the curve and show that it is isomorphic to Klein's four ...
On the nonexistence of almost Moore digraphs
(2014-07-01)
Article.
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Article.
Accés restringit per política de l'editorial
Digraphs of maximum out-degree at most d > 1, diameter at most k > 1 and order N(d, k) = d + ... + d(k) are called almost Moore or (d, k)-digraphs. So far, the problem of their existence has been solved only when d = 2, 3 ...
Residual ideals of MacLane valuations
(2015)
Article.
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Article.
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Let K be a field equipped with a discrete valuation v. In a pioneering work,
MacLane determined all valuations on K(x) extending v. His work was recently reviewed
and generalized by Vaqui´e, by using the graded algebra ...
Single-factor lifting and factorization of polynomials over local fields
(2012-11)
Article.
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Article.
Accés obert
Let f (x) be a separable polynomial over a local field. The Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In this paper, we develop an ...
Genetics of polynomials over local fields
(2015)
Article.
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Article.
Accés obert
Let (K, v) be a discrete valued field with valuation ring O, and let Ov be the completion of O with respect to the v-adic topology. In this paper we discuss the advantages of manipulating polynomials in Ov[x] on a computer ...
Nonexistence of almost Moore digraphs of diameter four
(2013-03-31)
Article.
Accés obert
Article.
Accés obert
Regular digraphs of degree d > 1, diameter k > 1 and order N(d; k) = d+ +dk
will be called almost Moore (d; k)-digraphs. So far, the problem of their existence
has only been solved when d = 2; 3 or k = 2; 3. In this ...