82 research outputs found
Points de Stark-Heegner et fonctions L p-adiques
No full textLet K|Q be a number field and let ζK(s) be its associated complex L-function. The analytic class number formula relates special values of ζK(s) with algebraic invariants of the field K itself. It admits a Galois equivariant refinement known as Stark conjectures. We have a very similar picture in the case of elliptic curves. Let E/Q be an elliptic curve and let L(E/Q, s) be its associated complex L-function. The conjecture of Birch and Swinnerton-Dyer relates the behaviour of L(E/Q, s) at s = 1 to the structure of rational solutions of the equation defined by E. The equivariant Birch and Swinnerton- Dyer conjecture is obtained including in the picture the action of Galois groups. The elliptic Stark conjecture formulated by H. Darmon, A. Lauder and V. Rotger purposes a p-adic analogue of the equivariant Birch and Swinnerton-Dyer conjecture, under several assumption. In their paper, the authors formulate the conjecture and prove it in some cases of good reduction of E at p using Garrett-Hida method and performing a factorization of p-adic L-functions. In this dissertation we focus on the elliptic Stark conjecture and we show how it is possible to extend the result of Darmon, Lauder and Rotger. In the case of good reduction of E at p we can slightly extend the result using Hida- Rankin method. This method also gives us a better control of the constants appearing in the result, thus yielding an explicit formula which contains invariants associated with the elliptic curve. To achieve the proof we mimic the main result of Darmon, Lauder and Rotger in our setting and we make use of a p-adic Gross-Zagier formula which relates special values of the Bertolini-Darmon-Prasanna p-adic L-function to Heegner points. In a second moment we extend both our result and Darmon-Lauder-Rotger result to the case of multi- plicative reduction of E at p. In this setting we cannot use Bertolini- Darmon Prasanna p-adic L-function due to some technical reasons. In order to avoid the problem we consider Castellà’s two variables p-adic L-function. We use both Garrett-Hida method and Hida-Rankin method. In the two cases we obtain formulae which are similar to those of the good reduction setting.Soit K|Q un corps de nombres et soit ζK(s) sa fonction L complexe associée. La formule analytique du nombre de classes fournit un lien entre les valeurs spéciales de ζK(s) et les invariants du corps K. Elle admet une version Galois-équivariante. On a un schema similaire pour les courbes elliptiques. Soit E/Q une courbe elliptique et soit L(E/Q, s) sa fonction L complexe associée. La conjecture de Birch et Swinnerton-Dyer prédit un lien entre le comportement de L(E/Q, s) au point s = 1 et la structure des solutions rationnelles de l’équation definie par E. Comme la formule analytique du nombre de classes, la conjecture de Birch et Swinnerton-Dyer admet une version équivariante. La conjecture de Stark elliptique formulée par H. Darmon, A. Lauder et V. Rotger propose un analogue p-adique de la conjecture de Birch et Swinnerton-Dyer équivariante, qui nécessite certaines hypothèses. Dans leur article, les auteurs formulent la conjecture et donnent une démonstration dans certains cas où E a bonne réduction en p. Pour cela, ils utilisent la méthode de Garrett-Hida qui conduit à une factorisation de fonctions L p-adiques. Dans cette thèse on se concentre sur la conjecture de Stark elliptique et l’on montre comme il est possible d’étendre le résultat de Darmon, Lauder et Rotger. Dans le cas où E a bonne réduction en p on peut étendre le résultat en utilisant la méthode de Hida- Rankin. Cette méthode nous donne un contrôle meilleur sur les constantes apparaissant dans les formules et nous amène à une formule explicite contenant les invariants de la courbe elliptique. Pour obtenir le résultat on adapte la preuve du théorème principal de Darmon, Lauder et Rotger à notre cas et on utilise une formule p-adique de Gross et Zagier qui relie les valeurs spéciales de la fonction L padique de Bertolini-Darmon-Prasanna et les points de Heegner. Ensuite on voit comment étendre notre résultat et celui de Darmon-Lauder-Rotger au cas où E a réduction multiplicative en p. Dans ce cadre, on ne peut pas utiliser la fonction L p-adique de Bertolini-Darmon-Prasanna en raison de problèmes techniques. Pour éliminer cette difficulté on consid`ere la fonction L p-adique de Castellà. On utilise aussi la méthode de Garrett-Hida ainsi que la méthode d’Hida-Rankin et l’on obtient des résultats similaires aux cas de bonne réduction
Colorado ground beetles (Coleoptera: Carabidae) from the Rotger Collection, University of Colorado Museum
No full textGround Beetles from Rotger\u27s collection of Colorado specimens have been identified, principally by the author, and a faunal list of 161 species from 80 localities is presented. The list includes 35 species not previously recorded from Colorado. Comparisons are made with Armin\u27s (1963) carabid list from Boulder County and the diversity of species along transects through four elevational zones from the plains to the alpine
On the elliptic Stark conjecture at primes of multiplicative reduction
No full textIn [DLR], Darmon, Lauder, and Rotger formulated a p-adic elliptic Stark conjecture for the twist of an elliptic curve E/Q by the self-dual tensor product ¿ ¿ of two odd and two-dimensional Artin representations. These authors provided abundant numerical evidence and proved the conjecture in the special setting where p is a prime of good reduction for E and ¿ and ¿2 are induced from finite-order characters ¿, ¿ of the same imaginary quadratic field. The key step in their proof is a factorization of one-variable p-adic L-functions, where ¿ varies in a p-adic family of Hecke characters. The main goal of this article is to prove a new case of the conjecture, placing ourselves in the setting where p is a prime of multiplicative reduction for E. In order to achieve our theorem, we need to work with two-variable p-adic L-functions, where the weight 2 cusp form associated with E also moves independently along a Hida family. Our main result then follows from a factorization of p-adic L-series extending to two variables the one obtained in [DLR]. On the way we also generalize to our setting the results obtained in [CR].Peer ReviewedPostprint (author's final draft
Stark-Heegner points and p-adic L-functions
No full textSoit K|Q un corps de nombres et soit ζK(s) sa fonction L complexe associée. La formule analytique du nombre de classes fournit un lien entre les valeurs spéciales de ζK(s) et les invariants du corps K. Elle admet une version Galois-équivariante. On a un schema similaire pour les courbes elliptiques. Soit E/Q une courbe elliptique et soit L(E/Q, s) sa fonction L complexe associée. La conjecture de Birch et Swinnerton-Dyer prédit un lien entre le comportement de L(E/Q, s) au point s = 1 et la structure des solutions rationnelles de l’équation definie par E. Comme la formule analytique du nombre de classes, la conjecture de Birch et Swinnerton-Dyer admet une version équivariante. La conjecture de Stark elliptique formulée par H. Darmon, A. Lauder et V. Rotger propose un analogue p-adique de la conjecture de Birch et Swinnerton-Dyer équivariante, qui nécessite certaines hypothèses. Dans leur article, les auteurs formulent la conjecture et donnent une démonstration dans certains cas où E a bonne réduction en p. Pour cela, ils utilisent la méthode de Garrett-Hida qui conduit à une factorisation de fonctions L p-adiques. Dans cette thèse on se concentre sur la conjecture de Stark elliptique et l’on montre comme il est possible d’étendre le résultat de Darmon, Lauder et Rotger. Dans le cas où E a bonne réduction en p on peut étendre le résultat en utilisant la méthode de Hida- Rankin. Cette méthode nous donne un contrôle meilleur sur les constantes apparaissant dans les formules et nous amène à une formule explicite contenant les invariants de la courbe elliptique. Pour obtenir le résultat on adapte la preuve du théorème principal de Darmon, Lauder et Rotger à notre cas et on utilise une formule p-adique de Gross et Zagier qui relie les valeurs spéciales de la fonction L padique de Bertolini-Darmon-Prasanna et les points de Heegner. Ensuite on voit comment étendre notre résultat et celui de Darmon-Lauder-Rotger au cas où E a réduction multiplicative en p. Dans ce cadre, on ne peut pas utiliser la fonction L p-adique de Bertolini-Darmon-Prasanna en raison de problèmes techniques. Pour éliminer cette difficulté on consid`ere la fonction L p-adique de Castellà. On utilise aussi la méthode de Garrett-Hida ainsi que la méthode d’Hida-Rankin et l’on obtient des résultats similaires aux cas de bonne réduction.Let K|Q be a number field and let ζK(s) be its associated complex L-function. The analytic class number formula relates special values of ζK(s) with algebraic invariants of the field K itself. It admits a Galois equivariant refinement known as Stark conjectures. We have a very similar picture in the case of elliptic curves. Let E/Q be an elliptic curve and let L(E/Q, s) be its associated complex L-function. The conjecture of Birch and Swinnerton-Dyer relates the behaviour of L(E/Q, s) at s = 1 to the structure of rational solutions of the equation defined by E. The equivariant Birch and Swinnerton- Dyer conjecture is obtained including in the picture the action of Galois groups. The elliptic Stark conjecture formulated by H. Darmon, A. Lauder and V. Rotger purposes a p-adic analogue of the equivariant Birch and Swinnerton-Dyer conjecture, under several assumption. In their paper, the authors formulate the conjecture and prove it in some cases of good reduction of E at p using Garrett-Hida method and performing a factorization of p-adic L-functions. In this dissertation we focus on the elliptic Stark conjecture and we show how it is possible to extend the result of Darmon, Lauder and Rotger. In the case of good reduction of E at p we can slightly extend the result using Hida- Rankin method. This method also gives us a better control of the constants appearing in the result, thus yielding an explicit formula which contains invariants associated with the elliptic curve. To achieve the proof we mimic the main result of Darmon, Lauder and Rotger in our setting and we make use of a p-adic Gross-Zagier formula which relates special values of the Bertolini-Darmon-Prasanna p-adic L-function to Heegner points. In a second moment we extend both our result and Darmon-Lauder-Rotger result to the case of multi- plicative reduction of E at p. In this setting we cannot use Bertolini- Darmon Prasanna p-adic L-function due to some technical reasons. In order to avoid the problem we consider Castellà’s two variables p-adic L-function. We use both Garrett-Hida method and Hida-Rankin method. In the two cases we obtain formulae which are similar to those of the good reduction setting
Stark-Heegner points and p-adic L-functions
No full textSoit K|Q un corps de nombres et soit ζK(s) sa fonction L complexe associée. La formule analytique du nombre de classes fournit un lien entre les valeurs spéciales de ζK(s) et les invariants du corps K. Elle admet une version Galois-équivariante. On a un schema similaire pour les courbes elliptiques. Soit E/Q une courbe elliptique et soit L(E/Q, s) sa fonction L complexe associée. La conjecture de Birch et Swinnerton-Dyer prédit un lien entre le comportement de L(E/Q, s) au point s = 1 et la structure des solutions rationnelles de l’équation definie par E. Comme la formule analytique du nombre de classes, la conjecture de Birch et Swinnerton-Dyer admet une version équivariante. La conjecture de Stark elliptique formulée par H. Darmon, A. Lauder et V. Rotger propose un analogue p-adique de la conjecture de Birch et Swinnerton-Dyer équivariante, qui nécessite certaines hypothèses. Dans leur article, les auteurs formulent la conjecture et donnent une démonstration dans certains cas où E a bonne réduction en p. Pour cela, ils utilisent la méthode de Garrett-Hida qui conduit à une factorisation de fonctions L p-adiques. Dans cette thèse on se concentre sur la conjecture de Stark elliptique et l’on montre comme il est possible d’étendre le résultat de Darmon, Lauder et Rotger. Dans le cas où E a bonne réduction en p on peut étendre le résultat en utilisant la méthode de Hida- Rankin. Cette méthode nous donne un contrôle meilleur sur les constantes apparaissant dans les formules et nous amène à une formule explicite contenant les invariants de la courbe elliptique. Pour obtenir le résultat on adapte la preuve du théorème principal de Darmon, Lauder et Rotger à notre cas et on utilise une formule p-adique de Gross et Zagier qui relie les valeurs spéciales de la fonction L padique de Bertolini-Darmon-Prasanna et les points de Heegner. Ensuite on voit comment étendre notre résultat et celui de Darmon-Lauder-Rotger au cas où E a réduction multiplicative en p. Dans ce cadre, on ne peut pas utiliser la fonction L p-adique de Bertolini-Darmon-Prasanna en raison de problèmes techniques. Pour éliminer cette difficulté on consid`ere la fonction L p-adique de Castellà. On utilise aussi la méthode de Garrett-Hida ainsi que la méthode d’Hida-Rankin et l’on obtient des résultats similaires aux cas de bonne réduction.Let K|Q be a number field and let ζK(s) be its associated complex L-function. The analytic class number formula relates special values of ζK(s) with algebraic invariants of the field K itself. It admits a Galois equivariant refinement known as Stark conjectures. We have a very similar picture in the case of elliptic curves. Let E/Q be an elliptic curve and let L(E/Q, s) be its associated complex L-function. The conjecture of Birch and Swinnerton-Dyer relates the behaviour of L(E/Q, s) at s = 1 to the structure of rational solutions of the equation defined by E. The equivariant Birch and Swinnerton- Dyer conjecture is obtained including in the picture the action of Galois groups. The elliptic Stark conjecture formulated by H. Darmon, A. Lauder and V. Rotger purposes a p-adic analogue of the equivariant Birch and Swinnerton-Dyer conjecture, under several assumption. In their paper, the authors formulate the conjecture and prove it in some cases of good reduction of E at p using Garrett-Hida method and performing a factorization of p-adic L-functions. In this dissertation we focus on the elliptic Stark conjecture and we show how it is possible to extend the result of Darmon, Lauder and Rotger. In the case of good reduction of E at p we can slightly extend the result using Hida- Rankin method. This method also gives us a better control of the constants appearing in the result, thus yielding an explicit formula which contains invariants associated with the elliptic curve. To achieve the proof we mimic the main result of Darmon, Lauder and Rotger in our setting and we make use of a p-adic Gross-Zagier formula which relates special values of the Bertolini-Darmon-Prasanna p-adic L-function to Heegner points. In a second moment we extend both our result and Darmon-Lauder-Rotger result to the case of multi- plicative reduction of E at p. In this setting we cannot use Bertolini- Darmon Prasanna p-adic L-function due to some technical reasons. In order to avoid the problem we consider Castellà’s two variables p-adic L-function. We use both Garrett-Hida method and Hida-Rankin method. In the two cases we obtain formulae which are similar to those of the good reduction setting
SPECTROSCOPY OF MOLECULES: TENSORIAL FORMALISM ADAPTED TO THE CHAIN, HAMILTONIAN AND TRANSITION MOMENT OPERATORS. APPLICATION TO THE and BANDS OF .
No full textW. Raballand, M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., accepted (2003). J.-P. Champion, M. Lo\""{e}te and G. Pierre, in ""Spectroscopy of the Earth's Atmosphere and Interstellar Medium"" (K. N. Rao and A. Weber, Eds.) pp. 339-422, Academic Press, Inc., San Diego (1992). M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 200, 123-130, (2000). M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 200, 131-137, (2000). M. Rotger, V. Boudon and M. Lo\""{e}te, J. Mol. Spectrosc., 216, 297-307, (2002). B. G. Sartakov, J. Oomens, J. Reuss and A. Fayt, J. Mol. Spectrosc., 185, 31-47 (1997).Author Institution: Laboratoire de Physique de I'Universit\'{e} de BourgogneA tensorial formalism adapted to the case of asymmetric with symmetry has been developed in the same way as in the previous works on and spherical symmetric or asymmetric . We use the group chain. The method is similar to that already outlined by Sartakov . All the coupling coefficients and formulas for the computation of matrix elements are given for this chain. Such relations are then expressed in the group itself. We also present a development of the Hamiltonian, dipole moment, and polarizability operators for this type of molecules. Expressions of the matrix elements are derived for these operators. Two preliminary applications are presented. One concerns the infrared active band of the molecule and the other the Raman active band
Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture
No full textWe study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rathergeneral type of quaternionic orders. We address several questions arising from the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In particular, under mild technical conditions, we show the existence of non-torsion Heegner points on elliptic curves in all situations in which the BSD conjecture predicts their existence
SYMMETRY-ADAPTED TENSORIAL FORMALISM FOR THE SPECTROSCOPY OF THE QUASISPHERICAL TOP: APPLICATION TO THE BENDING TRIAD
No full textM. Rotger, V. Boudon and M. Lo\'{e}te, J. Mol. Spectrosc., 216, 297-307, (2002). M. Rotger, V. Boudon, M. Lo\'{e}te, L. Margul\""{e}s, J. Demaison, H. M\""{a}der, G. Winnewisser and H.S.P. M\""{u}ller, J. Mol. Spectrosc., 222, 172-179, (2003). H. B\""{u}rger, J. Demaison, F. Hegelund, L. Margul\""{e}s, I. Merke, J. Mol. Struct., 612, 133-141, (2002).Author Institution: Laboratoire de Physique de l'Universit\'{e} de BourgogneThe techniques of symmetry-adapted tensorial formalism and of vibrational extrapolation developed since many years by the Dijon group have proved their efficiency for the spectroscopy of spherical-top molecules . We have extended these methods to the case of quasi-spherical tops such as . This model has been used recently to perform the analysis of the ground state of this . We present here a preliminary study concerning the analysis of the bending triad in the region. These results are compared to those obtained with the usual asymmetric-top . A set of programs for spectrum calculations and fits named TDS has been used and is freely available at the URL: http://www.u-bourgogne.fr/LPUB/c2vTDS.htm
Algorithms for chow-heegner points via iterated integrals
No full textLet 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.Peer ReviewedPostprint (updated version
EXTENSION OF THE STDS/HTDS SOFTWARE TO ROVIBRONIC SPECTROSCOPY AND TO LOWER SYMMETRY PROBLEMS
No full textCh. Wenger and J.-P. Champion, J. Quant. Spectrosc. Radiat. Transfer, 59, 471-480 (1998). Ch. Wenger, V. Boudon J.-P. Champion and G. Pierre, J. Quant. Spectrosc. Radiat. Transfer, 66, 1-16 (2000). M. Rey, V. Boudon, M. Lo\""ete and F. Michelot, J. Mol. Spectrosc., 204, 106-119 (2000). M. Rey, V. Boudon and M. Lo\""ete, J. Mol. Struct., in press (2001). M. Rotger, V. Boudon and M. Lo\""ete, J. Mol. Spectrosc., 200, 123-130 (2000). M. Rotger, V. Boudon and M. Lo\""ete, J. Mol. Spectrosc., 200, 131-137 (2000).Author Institution: Laboratoire de Physique de l'Universit\'e de BourgogneWe present new softwares using the group-theoretical and tensorial methods developed in the Dijon group. They are based on the Spherical Top Data System and the Highly-spherical Top Data System previously written for spherical-top molecules in a singlet electronic state. The two types of problems that can be handled with these new programs are: The case of spherical-top molecules in a degenerate electronic state. This concerns the rovibronic spectroscopy instead of the rovibrational spectroscopy, for species like or . A new formalism including electronic operators and rovibronic couplings has been and implemented in a new version of HTDS. The case of ``quasi spherical-top'' molecules of and symmetry. This concerns symmetric-top molecules deriving from spherical-tops by substitution of one ligand like ( symmetry) or asymmetric-tops with ligands having close masses like ( symmetry). New formalism using the and group chains have been developed and implemented into two new program suites named TDS and TDS, respectively. These software packages will be available soon for free download
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