TN - Teoria de Nombres
http://hdl.handle.net/2117/3728
2015-12-01T09:21:46ZOverconvergent generalised eigenforms of weight one and class fields of real quadratic fields
http://hdl.handle.net/2117/78762
Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields
Darmon, Henri; Lauder, Alan; Rotger Cerdà, Víctor
This article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the Hecke operators. When this generalised eigenspace contains the theta series attached to a character of a real quadratic field K in which the prime p splits, the coefficients of the attendant generalised eigenform are expressed as p-adic logarithms of algebraic numbers belonging to an idoneous ring class field of K. This suggests an approach to
2015-11-04T11:14:19ZDarmon, HenriLauder, AlanRotger Cerdà, VíctorThis article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the Hecke operators. When this generalised eigenspace contains the theta series attached to a character of a real quadratic field K in which the prime p splits, the coefficients of the attendant generalised eigenform are expressed as p-adic logarithms of algebraic numbers belonging to an idoneous ring class field of K. This suggests an approach toAlgorithms for chow-heegner points via iterated integrals
http://hdl.handle.net/2117/78758
Algorithms for chow-heegner points via iterated integrals
Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger Cerdà, Víctor
Let E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, PT,f ¿ E(Q), indexed by algebraic correspondences T ¿ X0(N) × X0(N). It also gives an analytic formula, depending only on the image of T in cohomology under the complex cycle class map, for calculating PT,f numerically via Chen's theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor N < 100 when the cycles T arise from Hecke correspondences, and discusses several important variants of the basic construction.
2015-11-04T10:59:38ZDarmon, HenriDaub, MichaelLichtenstein, SamRotger Cerdà, VíctorLet E/Q be an elliptic curve of conductor N and let f be the weight 2 newform on G0(N) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols describes the construction of so-called Chow-Heegner points, PT,f ¿ E(Q), indexed by algebraic correspondences T ¿ X0(N) × X0(N). It also gives an analytic formula, depending only on the image of T in cohomology under the complex cycle class map, for calculating PT,f numerically via Chen's theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor N < 100 when the cycles T arise from Hecke correspondences, and discusses several important variants of the basic construction.Non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras
http://hdl.handle.net/2117/28490
Non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras
Crespo, Teresa; Río Doval, Ana; Vela del Olmo, Mª Montserrat
We give a degree 8 non-normal separable extension having two non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras.
2015-07-01T11:16:43ZCrespo, TeresaRío Doval, AnaVela del Olmo, Mª MontserratWe give a degree 8 non-normal separable extension having two non-isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras.Genetics of polynomials over local fields
http://hdl.handle.net/2117/28206
Genetics of polynomials over local fields
Guàrdia Rubies, Jordi; Nart Vinyals, Enric
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 by means of OM representations of prime (monic and irreducible) polynomials. An OM representation supports discrete data characterizing the Okutsu equivalence class of the prime polynomial. These discrete parameters are a kind of DNA sequence common to all individuals in the same Okutsu
class, and they contain relevant arithmetic information about the polynomial
and the extension of Kv that it determines
2015-06-05T15:29:48ZGuàrdia Rubies, JordiNart Vinyals, EnricLet (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 by means of OM representations of prime (monic and irreducible) polynomials. An OM representation supports discrete data characterizing the Okutsu equivalence class of the prime polynomial. These discrete parameters are a kind of DNA sequence common to all individuals in the same Okutsu
class, and they contain relevant arithmetic information about the polynomial
and the extension of Kv that it determinesResidual ideals of MacLane valuations
http://hdl.handle.net/2117/28203
Residual ideals of MacLane valuations
Fernández González, Julio; Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric
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 of a valuation. We extend Vaqui´e’s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of
the theory. As a consequence, we determine the structure of the graded algebra of the
discrete valuations on K(x) and we show how these valuations may be used to parameterize
irreducible polynomials over local fields up to Okutsu equivalence
2015-06-05T14:57:13ZFernández González, JulioGuàrdia Rubies, JordiMontes Peral, JesúsNart Vinyals, EnricLet 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 of a valuation. We extend Vaqui´e’s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of
the theory. As a consequence, we determine the structure of the graded algebra of the
discrete valuations on K(x) and we show how these valuations may be used to parameterize
irreducible polynomials over local fields up to Okutsu equivalenceHigher Newton polygons and integral bases
http://hdl.handle.net/2117/28202
Higher Newton polygons and integral bases
Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric
Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K atp. The Montes algorithm factorizes a monic irreducible separable polynomial f(x) ∈ A[x] over Kp, and it provides essential arithmetic information about the finite extensions of Kp determined by the different irreducible factors. In
particular, it can be used to compute a p-integral basis of the extension of K determined by f(x). In this paper we present a new and faster method to compute p-integral bases, based on the use of the quotients of certain divisions with remainder of f(x) that occur along the flow of the Montes algorithm
2015-06-05T14:44:46ZGuàrdia Rubies, JordiMontes Peral, JesúsNart Vinyals, EnricLet A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K atp. The Montes algorithm factorizes a monic irreducible separable polynomial f(x) ∈ A[x] over Kp, and it provides essential arithmetic information about the finite extensions of Kp determined by the different irreducible factors. In
particular, it can be used to compute a p-integral basis of the extension of K determined by f(x). In this paper we present a new and faster method to compute p-integral bases, based on the use of the quotients of certain divisions with remainder of f(x) that occur along the flow of the Montes algorithmA new computational approach to ideal theory in number fields
http://hdl.handle.net/2117/28201
A new computational approach to ideal theory in number fields
Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric
Let K be the number field determined by a monic irreducible polynomial f(x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f(x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these constructive representations
of the prime ideals. From a computational perspective, these results facilitate
the manipulation of fractional ideals of K avoiding two heavy tasks: the construction
of the maximal order of K and the factorization of the discriminant
of f(x). The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals
2015-06-05T14:02:14ZGuàrdia Rubies, JordiMontes Peral, JesúsNart Vinyals, EnricLet K be the number field determined by a monic irreducible polynomial f(x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f(x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these constructive representations
of the prime ideals. From a computational perspective, these results facilitate
the manipulation of fractional ideals of K avoiding two heavy tasks: the construction
of the maximal order of K and the factorization of the discriminant
of f(x). The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime idealsCom explicar un sistema CLIL: un model dinàmic newtonià
http://hdl.handle.net/2117/27398
Com explicar un sistema CLIL: un model dinàmic newtonià
Alsina Aubach, Montserrat
En la implementació del CLIL a l’educació superior, apart d’estudis sobre el nivell de l’estudiantat i la disponibilitat del professorat, i de l’elaboració de
material educatiu interdisciplinari, el repte actual és aconseguir que s’involucrin activament en CLIL els professors de contingut d’un ventall ampli de disciplines. En aquesta comunicació es presenten les bases d’un
model per un sistema CLIL, utilitzant la dinàmica newtoniana. Pot ser un model interessant i plausible en un context universitari científic i tecnològic, on fins ara el CLIL s’ha implementat només lleugerament.
2015-04-16T16:53:44ZAlsina Aubach, MontserratEn la implementació del CLIL a l’educació superior, apart d’estudis sobre el nivell de l’estudiantat i la disponibilitat del professorat, i de l’elaboració de
material educatiu interdisciplinari, el repte actual és aconseguir que s’involucrin activament en CLIL els professors de contingut d’un ventall ampli de disciplines. En aquesta comunicació es presenten les bases d’un
model per un sistema CLIL, utilitzant la dinàmica newtoniana. Pot ser un model interessant i plausible en un context universitari científic i tecnològic, on fins ara el CLIL s’ha implementat només lleugerament.Students' viewpoint on engineering subjects taugh in English
http://hdl.handle.net/2117/27362
Students' viewpoint on engineering subjects taugh in English
Heras Cisa, F. Xavier de las; Lao Luque, Concepción; Fortuny Santos, Jordi; Alsina Aubach, Montserrat
The European Educational Institutions have the challenge and the commitment to enhance multilingual competence and teaching curricular subjects in a foreign language is seen as one of the most promising alternatives.
In that context, professors teaching different engineering subjects at the School of Engineering of the UPC at Manresa (EPSEM) have been involved in projects aiming at analyzing the current linguistic situation and developing some on-line open access materials using CLIL as a strategy. They formed the u-Linguatech Research Group on Multilingual Communication in Science and Technology in order to provide such resources in an effective and efficient way.
In this paper, we focus on students’ perception of the improvement of their
multilingual competence throughout their Engineering degree, by means of
subjects taught in English by non-native speakers. Data about the English level of current students are taken into account. We also describe the use of the above resources to improve the quality of subjects learning related to Chemical Engineering curricula.
2015-04-15T15:55:40ZHeras Cisa, F. Xavier de lasLao Luque, ConcepciónFortuny Santos, JordiAlsina Aubach, MontserratThe European Educational Institutions have the challenge and the commitment to enhance multilingual competence and teaching curricular subjects in a foreign language is seen as one of the most promising alternatives.
In that context, professors teaching different engineering subjects at the School of Engineering of the UPC at Manresa (EPSEM) have been involved in projects aiming at analyzing the current linguistic situation and developing some on-line open access materials using CLIL as a strategy. They formed the u-Linguatech Research Group on Multilingual Communication in Science and Technology in order to provide such resources in an effective and efficient way.
In this paper, we focus on students’ perception of the improvement of their
multilingual competence throughout their Engineering degree, by means of
subjects taught in English by non-native speakers. Data about the English level of current students are taken into account. We also describe the use of the above resources to improve the quality of subjects learning related to Chemical Engineering curricula.Asignaturas de Electrònica en la EPSEM: planificación de la impartición en inglés
http://hdl.handle.net/2117/27359
Asignaturas de Electrònica en la EPSEM: planificación de la impartición en inglés
Alsina Aubach, Montserrat; Argelaguet Isanta, María Rosa; Vicente Rodrigo, Jesús; Martínez Teixidor, Inmaculada
Al objeto de garantizar la calidad del aprendizaje de la Electrónica en los estudios de Grado impartidos en la EPSEM, es necesario planificar de manera adecuada las asignaturas impartidas en inglés. En este trabajo se muestran los resultados del análisis realizado a los estudiantes que cursarán estas asignaturas, en el que se ponen de manifiesto las dificultades observadas y las expectativas generadas, motivando la elaboración de material de soporte específico.; In order to ensure the quality of learning of Electronics for graduate studies offered at the EPSEM, it is needed to plan properly the subjects taught in English. In this paper the results of the students analysis who will attend these courses are shown. These results reveal the difficulties encountered and the
expectations generated. This analysis motives the development of specific support material.
2015-04-15T15:43:15ZAlsina Aubach, MontserratArgelaguet Isanta, María RosaVicente Rodrigo, JesúsMartínez Teixidor, InmaculadaAl objeto de garantizar la calidad del aprendizaje de la Electrónica en los estudios de Grado impartidos en la EPSEM, es necesario planificar de manera adecuada las asignaturas impartidas en inglés. En este trabajo se muestran los resultados del análisis realizado a los estudiantes que cursarán estas asignaturas, en el que se ponen de manifiesto las dificultades observadas y las expectativas generadas, motivando la elaboración de material de soporte específico.
In order to ensure the quality of learning of Electronics for graduate studies offered at the EPSEM, it is needed to plan properly the subjects taught in English. In this paper the results of the students analysis who will attend these courses are shown. These results reveal the difficulties encountered and the
expectations generated. This analysis motives the development of specific support material.