Année
Publications
Voiles et polyèdres de Klein.
200 pp. environ, à paraître.
Isolated extremal points.
Journal of Convex Analysis, à paraître.
Jacobians among Abelian threefolds: a formula of Klein and a question of Serre.
Math. Res. Lett. 17, no. 2, 323--333 and Doklady Akademii Nauk, Vol. 431, No 3, 313--316, 2010.
253 k
Zéros des fonctions L et formes toriques.
ArXiv:0907.0536, 32 pp., 2009.
Corrigenda and addenda to: "Étale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields".
Moscow Math. Journal 9, n° 2, 431-438. arXiv:0808.2169, 2009
168 k
Arithmetic, Geometry, Cryptography and Coding Theory.
International Conference, November 5-9, 2007, CIRM, Marseilles, France. Contemporary Mathematics, CONM 487, American Mathematical Society, viii + 206 pp, 2009
2008
On some questions of Serre on abelian threefolds.
Algebraic Geometry and its applications (Tahiti, 2007), 88–-115, Ser. Number Theory Appl., 5, World Sci. Publ., Hackensack, NJ, 2008
270 k
2005
Ramanujan modular forms and the Klein quartic.
Moscow Math. Journal, vol. 5, no. 4, 829--856, october-december 2005.
403 k
The Klein quartic as a cyclic group generator.
Moscow Math. Journal, vol. 5, no. 4, 857--868, october-december 2005.
246 k
L'hypothèse de Riemann : le Graal des mathématiciens.
La Recherche Hors-Série n°20, août 2005.
601 k
Arithmetic, geometry and coding theory (AGCT 2003).
Papers from the European School "Algebraic Geometry and Information Theory" and the 9th International Conference (AGCT 2003) held in Marseille, May 2003. Edited by Yves Aubry and Gilles Lachaud. Séminaires et Congrès [Seminars and Congresses], 11. Société Mathématique de France, Paris. xviii+215 pp. ISBN: 2-85629-175-9, 2005.
Qu'est-ce qu'une équation ?
Notions, Encyclopœdia Universalis, 2004.
91 k
Spectral analysis and the Riemann hypothesis.
Proceedings of the International Conference on Special Functions and their Applications (Chennai, 2002). J. Comput. Appl. Math. 160, no. 1-2, 175--190, 2003.
199 k
Étale cohomology, Lefschetz theorems and number of points of singular varieties over finite fields.
Dedicated to Yuri I. Manin on the occasion of his 65th birthday. Moscow Mathematical Journal 2, no. 3, 589--631, 2002
506 k
Number of solutions of equations over finite fields and a conjecture of Lang and Weil.
Number theory and discrete mathematics (Chandigarh, 2000), 269--291, Trends Math., Birkhäuser, Basel, 2002.
321 k
Communiquer sans erreur : les codes correcteurs.
"L'explosion des mathématiques", SMF-SMAI, Paris, pp. 84--87, 2002.
202 k
Communicating without errors: error-correcting codes.
"L'explosion des mathématiques", SMF-SMAI, Paris, pp. 84--87, 2002.
220 k
Voiles et polyhèdres de Klein.
Act. Sci. Ind., 176 pp, Hermann, 2002.
Zéros des fonctions L et formes toriques.
C.R. Acad. Sci. Sér. I Math. 335, 219--222, 2002.
128 k
Hyperplane sections of Grassmannians and the number of MDS linear codes.
Finite Fields Appl. 7, no. 4, 468--506, 2001.
474 k
L'hypothèse de Riemann.
2,16 M
Group structure on projective spaces and cyclic codes over finite fields,
Finite Fields and Their Applications 6, no.2, pp.119-129 (available on Ideal), 2000
124 k
Un invariant birationnel des variétés de dimension 3 sur un corps fini [A birational invariant of 3-folds over a finite field],
J. Algebraic Geom. 9, no. 3, 451--458, 2000
Gauss problem for function fields.
J. Number Theory 85, no. 2, 109--129, 2000
228 k
Higher weights of Grassmann codes,
Coding theory, cryptography and related areas (Guanajuato, 1998), 122--131, Springer, Berlin, 2000
167 k
Analyse spectrale et hypothèse de Riemann
Prétirage de l'IML n. 99-16, 1999.
124 k
Lefschetz theorems and dependent rational points on curves over finite fields.
150 k
Sails and Klein polyhedra,
Number theory (Tiruchirapalli, 1996), 373--385, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998
Klein polygons and geometric diagrams,
Number theory (Tiruchirapalli, 1996), 365--372, Contemp. Math., 210, Amer. Math. Soc., Providence, RI, 1998
Lachaud Gilles and Tsfasman Michael A.
Formules explicites pour le nombre de points des variétés sur un corps fini [Explicit formulas for the number of points of varieties over a finite field],
J. Reine Angew. Math. 493, 1--60, 1997
357 k
Lachaud Gilles
Number of points of plane sections and linear codes defined on algebraic varieties,
Arithmetic, geometry and coding theory (Luminy, 1993), 77--104, de Gruyter, Berlin, 1996
Les codes correcteurs d'erreurs [Los codigos correctores de errores],
La Recherche, vol. 278, pp. 778-782 (Juillet-Août 1995) and also in Mundo Cientifico, vol. 161, pp. 864-868 (octobre 1995), 1995
[LV95b]
Special issue on algebraic geometry codes,
Edited by Gilles Lachaud, Michael A. Tsfasman, Jorn Justesen and Victor Keh-Wei Wei. IEEE Trans. Inform. Theory 41, no. 6, part 1. Institute of Electrical and Electronics Engineers, Inc. (IEEE), Chichester, pp. 1545--1772, 1995
Polynomial-time construction of codes. II. Spherical codes and the kissing number of spheres,
IEEE Trans. Inform. Theory 40, no. 4, 1140--1146, 1994
Polyèdre d'Arnold et voile d'un cône simplicial : analogues du théorème de Lagrange [The Arnold polyhedron and the sail of a simplicial cone : analogues of the Lagrange theorem],
C. R. Acad. Sci. Paris Sér. I Math. 317, no. 8, 711--716, 1993
Exponential sums as discrete Fourier transform with invariant phase functions,
Applied algebra, algebraic algorithms and error-correcting codes (San Juan, PR, 1993), 231--243, Lecture Notes in Comput. Sci., 673, Springer, Berlin, 1993
441 k
Artin-Schreier curves, exponential sums, and coding theory,
Discrete mathematics and applications to computer science (Marseille, 1989). Theoret. Comput. Sci. 94, no. 2, 295--310, 1992
Polynomial-time construction of codes. I. Linear codes with almost equal weights,
Appl. Algebra Engrg. Comm. Comput. 3, no. 2, 151--161, 1992
431 k
Polynomial-time construction of spherical codes.
Appl. Algebra Engrg. Comm. Comput. 3, no. 2, 151--161, 1991
276 k
Artin-Schreier curves, exponential sums, and the Carlitz-Uchiyama bound for geometric codes,
J. Number Theory 39, no. 1, 18--40, 1991
The weights of the orthogonals of the extended quadratic binary Goppa codes,
IEEE Trans. Inform. Theory 36, no. 3, 686--692, 1990
Nombre de points des jacobiennes sur un corps fini [Number of points of the Jacobian over a finite field],
Acta Arith. 56, no. 4, 329--340, 1990
Espaces différentiables singuliers et corps de nombres algébriques [Singular differentiable spaces and algebraic number fields],
Ann. Inst. Fourier (Grenoble) 40, no. 3, 723--737, 1990
1,12 M
The parameters of projective Reed-Muller codes,
Discrete Math. 81, no. 2, 217--221, 1990
Lachaud Gilles
Majoration de quelques sommes exponentielles.
Proc. Algebraic and Combinatorial Coding Theory (ACCT-2), pp. 127-132, IPPI, Moscow,1990.
Exponential sums and the Carlitz-Uchiyama bound,
Coding theory and applications (Toulon, 1988), 63--75, Lecture Notes in Comput. Sci., 388, Springer, New York-Berlin, 1989
435 k
Distribution of the weights of the dual of the Melas code.
Discrete Math. 79 (1989/90), pp. 103-106, 1989.
Projective Reed-Muller codes,
Coding theory and applications (Cachan, 1986), 125--129, Lecture Notes in Comput. Sci., 311, Springer, Berlin-New York, 1988
193 k
Exactitude et approximation en analyse diophantienne [Exactness and approximation in Diophantine analysis],
L'à-peu-près (Urbino, 1986), 27--45, Hist. Sci. Tech., 3, École Hautes Études Sci. Soc., Paris & Il Lavoro Editoriale, Ancona, 1988
Méthodes algébriques dans le codage de l'information.
Actes de la journée annuelle de la S.M.F. (1988), p. 25-43 ; = In Images des Mathématiques 1990", Courrier du C.N.R.S. 76 (1991), p. 50-58 ; = In "Codes Géométriques Algébriques et Arithmétique sur les Corps Finis", Journées Math. X-UPS 1993, École Polytechnique, Palaiseau, 1993, pp. 7-25. 1988.
Formes quadratiques, fractions continues, géodésiques hyperboliques et fonctions zêta.
Publications de l'I.R.M.A., U.L.P. Strasbourg, 19 pp., 1988.
Continued fractions, binary quadratic forms, quadratic fields, and zeta functions,
Algebra and topology 1988 (Taejon, 1988), 1--56, Korea Inst. Tech., Taejon, 1988
3,11 M
On real quadratic fields,
Bull. Amer. Math. Soc. (N.S.) 17, no. 2, 307--311, 1987
435 k
Sommes de Kloosterman, courbes elliptiques et codes cycliques en caractéristique 2 [Kloosterman sums, elliptic curves and cyclic codes in characteristic 2],
C. R. Acad. Sci. Paris Sér. I Math. 305, no. 20, 881--883, 1987
Sommes d'Eisenstein et nombre de points de certaines courbes algébriques sur les corps finis [Eisenstein sums and number of points of some algebraic curves over finite fields],
C. R. Acad. Sci. Paris Sér. I Math. 305, no. 16, 729--732, 1987
4,33 M
L'analyse diophantienne et le théorème de Faltings.
Quelques grands problèmes en mathématiques, Mathématiques à venir, Bull. S.M.F. 115, Supplément, pp. 46-49, 1987.
Continued fractions, binary quadratic forms, quadratic fields, and zeta functions,
Algebra and topology 1988 (Taejon, 1988), 1--56, Korea Inst. Tech., Taejon, 1987
3,11 M
Les codes géométriques de Goppa [The geometric Goppa codes],
Seminar Bourbaki, Vol. 1984/85. Astérisque No. 133-134, 189--207, 1986
1,41 M
Sur les corps quadratiques réels principaux [On principal real quadratic fields],
Séminaire de théorie des nombres, Paris 1984--85, 165--175, Progr. Math., 63, Birkhäuser Boston, Boston, MA, 1986
Diophante, Les Arithmétiques, livres IV à VII (texte arabe).
Notes math. t. III, Intr., pp. 85-206, t. IV, Intr., pp. 5-134. Coll. Guillaume Budé, Les Belles Lettres, Paris, 1984.
Lachaud Gilles
Calibre et fonctions Zêta des corps quadratiques réels.
Prépublication n° 63, L.A. 168 du C.N.R.S., Université de Nice, 23 pp., 1984.
Lachaud Gilles
What we can get from the History of Arithmetic.
Proc. of the 4th Int. Cong. on Math. Educ." (ICME IV) Berkeley, 1980, Birkhäuser, Boston, pp. 449-450, 1983.
Analyse spectrale et prolongement analytique : séries d'Eisenstein, fonctions zéta et nombre de solutions d'équations diophantiennes [Spectral analysis and analytic continuation : Eisenstein series, zeta functions and number of solutions of Diophantine equations],
Ann. Sci. Univ. Clermont-Ferrand II Math. No. 21, 1--14, 1982
811 k
An adelic proof of the Hardy-Littlewood Theorem on Waring's Problem. London Math. Soc. Lecture Notes Series n° 56, Cambridge University Press, pp. 343-349, 1982.
Scattering Theory and automorphic functions.
Proc. of the 6th International Conference in Mathematical Physics (Berlin, 1981), Mathematical Problems in Theoretical Physics, Lecture Notes in Physics 153, pp. 298-301, 1982.
Une présentation adélique de la série singulière et du problème de Waring [An adelic presentation of the singular series and the Waring problem],
Seminar on Number Theory, 1979--1980, Exp. No. 21, 32 pp., Univ. Bordeaux I, Talence, 1980 and also in Enseign. Math. (2) 28, no. 1-2, 139--169, 1980
1,91 M
Le prolongement analytique d'un type de fonctions zêta généralisées [The analytic continuation of a type of generalized zeta functions],
Journées Arithmétiques de Luminy (Colloq. Internat. CNRS, Centre Univ. Luminy, 1978), pp. 109--119, Astérisque, 61, Soc. Math. France, Paris, 1979
Nombres et archétypes : du vieux et du neuf [Number and archetypes: something old, something new],
Eleutheria, no. 2, 133--140, 1979
Variations sur un thème de Mahler,
Invent. Math. 52, no. 2, 149--162, 1979
867 k
Analyse spectrale des formes automorphes et séries d'Eisenstein,
Invent. Math. 46, no. 1, 39--79, 1978
3,37 M
Quelques points de l'Histoire de l'Arithmétique.
Chantiers Math. 37, pp. 12-20, 1977.
Propriétés asymptotiques des solutions d'équations simplement caractéristiques,
Séminaire Goulaouic-Schwartz 1975/1976 : Équations aux dérivées partielles et analyse fonctionnelle, Exp. No. 7, 16 pp. Centre Math., École Polytech., Palaiseau, 1976
1,08 M
Lachaud Gilles
Compte-rendu d'un cours d'Histoire de l'Arithmétique.
In "Histoire et Enseignement des Mathématiques", I.R.E.M. de l'Université de Poitiers (1977), 17 pp., 1976
Spectral analysis of automorphic forms on rank one groups by perturbation methods,
Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972), pp. 441--450. Amer. Math. Soc., Providence, R.I., 1973
Théorie spectrale.
Représentations des groupes localement compacts, Université Paris VII, 1969-1970. Secrétariat Mathématique de l'École Normale Supérieure, 1971.
