]. R. Traceachm, M. Achilles, and . Manaresi, residue currents and multidimensional residues, duality and division An exhaustive list of références Multiplicity for ideals of maximal analytic spread and intersection theory, J. Math. Kyoto Univ, vol.33, issue.4, pp.1029-1046, 1993.

]. R. Achr, S. Achilles, and . Rams, Intersection numbers, Segre numbers and generalized Samuel multiplicities, Arch. Math, vol.77, pp.391-398, 2001.

]. L. Alf, E. Alfonsi, and . Bézout, 1730-1783) : mathématicien, académicien, et professeur ausì ecle deslumì eres, thèse Université Paris 6, Décembre 2005. [Am] F. Amoroso, On a conjecture of C. Berenstein and A. Yger, Effective Methods in Algebraic Geometry, Proc. Mega'94 Algorithms in algebraic geometry and applications Progress in maths 143, pp.17-28, 1996.

A. Andreotti and F. Norguet, La convexité holomorphe dans l'espace des cycles d'une variété algébrique, Ann. Sc. Norm. Sup. Pisa, vol.21, pp.31-82, 1967.

M. Andersson, Residue currents and ideals of holomorphic functions, Bulletin des Sciences Math??matiques, vol.128, issue.6, pp.481-512, 2004.
DOI : 10.1016/j.bulsci.2004.03.003

M. Andersson, Le probl??me d???appartenance pour les id??aux de polyn??mes en termes de courants r??sidus, Annales de l???institut Fourier, vol.56, issue.1, pp.101-119, 2006.
DOI : 10.5802/aif.2174

M. Andersson, Residues of holomorphic sections and lelong currents, Arkiv f??r Matematik, vol.43, issue.2, pp.201-219, 2005.
DOI : 10.1007/BF02384777

M. Andersson, Explicit versions of the Briançon-Skoda theorem with variations, Michigan Math, J, vol.54, pp.361-373, 2006.

M. Andersson and E. Wulcan, Noetherian residue currents, preprint, disponible on Archiv, math, p.511237

]. F. Apj, J. P. Apéry, and . Jouanolou, Elimination -Le cas d'une variable Resolution of singularities and division of distributions, Mathématiques LMD- Master Commun. Pure Appl. Math, vol.23, pp.145-150, 1970.

]. A. Ats, A. Alexandrov, and . Tsikh, Théorie des résidus de Leray et formes de Barlet sur une intersectioncompì etesingulì ere, Comptes rendus de l'Académie des Sciences Paris, Série I, t, pp.333-334, 2001.

. A. Ay-]-l, A. P. Aizenberg, and . Yuzhakov, Integral representation and residues in Multidimensional complex analysis, 1983.

D. Barlet, Développements asymptotiques des fonctions obtenues par intégration sur les fibres, Inventiones math, pp.129-174, 1982.
DOI : 10.1007/bfb0097053

]. D. Bar2 and . Barlet, Le faisceau ? ? X sur un espace analytique X de dimension pure, Lecture Notes in Math, vol.670, pp.187-204, 1978.

D. Bernstein, The number of roots of a system of equations, Functional Analysis and its applications, pp.183-185, 1975.

]. S. Berg and . Bergman, ¨ Uber eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen , Recueil math, Soc. math. Moscou (Mat. Sbornik) , N. S., t, vol.1, issue.43, pp.851-862, 1936.

]. I. Bern and . Bernstein, Analytic continuation of generalized functions with respect to a parameter, Functional Anal, Appl, vol.6, pp.273-285, 1972.

. A. Bg-]-c, . Berenstein, and . Gay, Complex Variables, an Introduction, 1991.

[. Bost, H. Gillet, and C. Soulé, Heights of projective varieties and positive Green forms, Journal of the American Mathematical Society, vol.7, issue.4, pp.903-1027, 1994.
DOI : 10.1090/S0894-0347-1994-1260106-X

. A. Bgvy-]-c, R. Berenstein, A. Gay, A. Vidras, and . Yger, Residue currents and Bézout identities, Progress in Mathematics, vol.114, 1993.

D. Barlet and H. M. Maire, Développements asymptotiques, transformation de Mellin complexe et intégration sur les fibres, Séminaire Lelong-Skoda 1985-86, Lecture Notes, vol.1295, pp.11-23
DOI : 10.1007/bfb0081975

H. Biosca, J. Briançon, and H. Maynadier, Espaces conormaux relatifs. II. Modules diff??rentiels, Publications of the Research Institute for Mathematical Sciences, vol.34, issue.2, pp.123-134, 1998.
DOI : 10.2977/prims/1195144757

J. E. Björk, Rings of of differential operators, North-Holland, 1979.

J. E. Björk, Analytic D-modules and applications, Mathematics and its Applications, 1993.

J. E. Björk, Residues and D-modules. The legacy of Niels Henrik Abel, pp.605-651, 2004.

J. Y. Boyer and M. Hickel, Une g??n??ralisation de la loi de transformation pour les r??sidus, Bulletin de la Société mathématique de France, vol.125, issue.3, pp.315-335, 1997.
DOI : 10.24033/bsmf.2309
URL : http://archive.numdam.org/article/BSMF_1997__125_3_315_0.pdf

J. Y. Boyer and M. Hickel, Extension dans un cadre algébrique d'une formule de Weil, manuscripta math, pp.1-29, 1999.
DOI : 10.1007/s002290050135

J. Briançon, Espaces conormaux relatifs I : Conditions de transversalit??, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.30, issue.5, pp.675-692, 1997.
DOI : 10.1016/S0012-9593(97)89935-1

J. Briançon and H. Skoda, Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de C n , Comptes Rendus Acad, Sciences Paris, Sér. A, pp.278-949, 1974.

D. W. Brownawell, Bounds for the Degrees in the Nullstellensatz, The Annals of Mathematics, vol.126, issue.3, pp.577-591, 1987.
DOI : 10.2307/1971361

]. B. Buch and . Buchberger, An algorithmic method in polynomial ideal theory, Multidimensional systems theory, 1985.

C. A. Berenstein, A. Vidras, and A. Yger, Analytic residues along algebraic cycles, Journal of Complexity, vol.21, issue.1, pp.5-42, 2005.
DOI : 10.1016/j.jco.2004.03.006
URL : https://hal.archives-ouvertes.fr/hal-00281544

C. A. Berenstein and A. Yger, Effective Bezout identities in Q[z1, ..., zn], Acta Mathematica, vol.166, issue.0, pp.69-120, 1991.
DOI : 10.1007/BF02398884

C. A. Berenstein and A. Yger, Residue calculus and effective Nullstellensatz, American Journal of Mathematics, vol.121, issue.4, pp.723-796, 1999.
DOI : 10.1353/ajm.1999.0026
URL : http://drum.lib.umd.edu/bitstream/1903/5758/1/TR_96-39.pdf

C. A. Berenstein and A. Yger, Green currents and analytic continuation, Journal d'Analyse Math??matique, vol.24, issue.2, pp.1-50, 1998.
DOI : 10.1007/BF02788690
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.324.3299

C. A. Berenstein and A. Yger, Residue currents, integration currents in the non complete intersection case, J. reine. angew. Math, vol.527, pp.203-235, 2000.

D. [. Cattani, A. Cox, and . Dickenstein, Residues in toric varieties, Compositio Mathematica, vol.108, issue.1, pp.35-76, 1997.
DOI : 10.1023/A:1000180417349

E. Cattani and A. Dickenstein, A global view of residues in the torus in Algorithms for algebra, J. Pure Appl. Algebra, vol.117118, pp.119-144, 1996.

A. [. Cattani, B. Dickenstein, and . Sturmfels, Computing multidimensional residues in Algorithms in algebraic geometry and applications, Progr. Math, vol.143, pp.135-164, 1994.

D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra, Undergraduate Texts in Mathematics, 1997.

D. Cox, J. Little, and D. Shea, Using algebraic geometry, Graduate Texts in Mathematics, vol.185, 2005.
DOI : 10.1007/978-1-4757-6911-1

D. A. Cox, Erratum to ???The homogeneous coordinate ring of a toric variety???, Journal of Algebraic Geometry, vol.23, issue.2, pp.17-50, 1995.
DOI : 10.1090/S1056-3911-2013-00651-7

D. A. Cox, Toric residues, Arkiv f??r Matematik, vol.34, issue.1, pp.73-96, 1996.
DOI : 10.1007/BF02559508

E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math, vol.69, issue.3, pp.287-299, 1998.

]. E. Cykt, T. Cygan, P. Krasi´nskikrasi´nski, and . Tworzewski, Separation of algebraic sets and the Lojasiewicz exponent of a polynomial mapping, Inventiones math, pp.75-87, 1999.

]. N. Coh, M. Coleff, and . Herrera, Les courants résiduels associésassociésà une forme méromorphe, Lecture Notes in Math, vol.633, 1978.

J. P. Demailly, Courants positifs et théorie de l'intersection, Gaz. Math. No, vol.53, pp.131-159, 1992.
DOI : 10.1007/bf01389359

J. P. Demailly, Nombres de Lelong généralisés, théorèmes d'intégrabilité et d'analyticité, Acta Math, pp.153-169, 1987.
DOI : 10.1007/bf02392558

J. P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in Complex Analysis and Geometry, Univ, Series in Math, 1993.

J. P. Demailly and M. Passare, Courants résiduels et classe fondamentale, Bull. Sci. Math, vol.119, pp.85-94, 1995.

G. Doetsch, Introduction to the theory and applications of the Laplace Transformations De Rham, Relations entre la topologie et la théorie des intégrales multiples, Ens. math, vol.35, pp.213-228, 1936.

G. [. Dwork, F. J. Gerotto, and . Sullivan, An introduction to G-functions, Annals of Mathematics Studies, vol.133, 1994.

]. D. Eis and . Eisenbud, Commutative algebra, with a view toward algebraic geometry, Graduate Texts in Mathematics, vol.150, 1995.

M. Elkadi, Une version effective du théoréme de Briançon-Skoda dans le cas algébrique discret, Acta Arithm, vol.66, pp.20-220, 1994.

M. Elkadi and A. Yger, Residue Calculus and Applications, Publications of the Research Institute for Mathematical Sciences, vol.43, issue.1, pp.55-74, 2007.
DOI : 10.2977/prims/1199403807
URL : https://hal.archives-ouvertes.fr/hal-00281540

. D. El, H. Eisenbud, and . Levine, An algebraic formula for the degree of a C ? map germ, Ann. of Math, vol.106, pp.19-44, 1977.

]. L. Einl, R. Ein, and . Lazarsfeld, A geometric effective Nullstellensatz, Inventiones math, pp.427-448, 1999.

G. Faltings, Diophantine Approximation on Abelian Varieties, The Annals of Mathematics, vol.133, issue.3, pp.549-576, 1991.
DOI : 10.2307/2944319

W. Fulton, Introduction to intersection theory in Algebraic Geometry, 1984.
DOI : 10.1090/cbms/054

W. Fulton, Intersection theory, 1984.

W. Fulton, Introduction to toric varieties, 1993.
DOI : 10.1515/9781400882526

P. Griffiths, J. Harris, . M. Gkz-]-i, M. M. Gelfand, A. V. Kapranov et al., Principles of Algebraic Geometry, 1978.
DOI : 10.1002/9781118032527

P. Griffiths, On the periods of certain rational integrals, I, Ann, Math, vol.90, pp.460-495, 1969.

P. Griffiths, Variations on a theorem of Abel, Inventiones math, pp.321-390, 1976.

. C. Gr-]-r, H. Gunning, and . Rossi, Analytic Functions of Several Complex Variables, N.J, 1985.

H. Gillet and C. Soulé, Arithmetic intersection theory, Publications math??matiques de l'IH??S, vol.83, issue.3, pp.72-93, 1990.
DOI : 10.1007/BF02699132

R. Hartshorne, A. Geometry, and R. Harvey, Integral formulae connected by Dolbeault's isomorphism, Ha2] R. Hartshorne, Residues and duality, pp.77-97, 1970.

G. Henkin and M. Passare, Abelian differentials on singular varieties and variation on a theorem of Lie-Griffiths, Inventiones math, pp.297-328, 1999.

]. A. Heny, A. Hénaut, and . Yger, Eléments de géométrie, Editions Ellipses, Die Frage der endlich vielen Schritte in der theorie der polynomideale, Math. Ann. 95, pp.736-788, 1926.

M. Hochster and C. Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc, vol.3, pp.31-116, 1990.

H. Hironaka, Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II, The Annals of Mathematics, vol.79, issue.2, pp.79-109, 1964.
DOI : 10.2307/1970547

M. Herrera and D. Lieberman, Residues and principal values on complex spaces, Mathematische Annalen, vol.64, issue.4
DOI : 10.1007/BF01350129
URL : http://www.digizeitschriften.de/download/PPN235181684_0194/PPN235181684_0194___log50.pdf

P. Jeanquartier, Développement asymtotique de la distribution de Dirac associéè a une fonction analytique, Comptes Rendus Acad. sci. Paris, vol.278, pp.949-951, 1974.

]. C. Jac and . Jacobi, Theoremata nova algebraica circa systema duarum aequationum inter duas variabiles propositarum, Crelle Journal für die reine und angewandte Mathematik, pp.281-288

Z. Jelonek, On the effective Nullstellensatz, Inventiones math, pp.1-17, 2005.

M. Kashiwara, B?functions and holonomic systems, Inventiones math, pp.33-53, 1976.
DOI : 10.1007/bf01390168

A. Khovanskii, N. Polyedra, . The-euler-jacobi, and . Formula, NEWTON POLYHEDRA AND THE EULER-JACOBI FORMULA, Russian Mathematical Surveys, vol.33, issue.6, pp.237-238, 1978.
DOI : 10.1070/RM1978v033n06ABEH003876

A. Khovanskii and O. A. , Gel'fond, Newton polyhedra and Grothendieck residues, Dokl. Akad. Nauk, vol.350, issue.3, pp.298-300, 1996.

A. Khovanskii and O. A. , Gel'fond, Toric geometry and Grothendieck residues, Mosc. Math. J, vol.2, issue.1, pp.99-112, 0199.

J. King, A residue formula for complex subvarieties, Proc. Carolina conf. on holomorphic mappings and minimal surfaces, pp.43-56, 1970.

J. Kollár, Effective Nullstellensatz for arbitrary ideals, Journal of the European Mathematical Society, vol.1, issue.3, pp.313-337, 1999.
DOI : 10.1007/s100970050009

T. Krick, L. M. Pardo, and M. Sombra, Sharp estimates for the arithmetic Nullstellensatz, Duke Math, J, vol.109, issue.3, pp.521-598, 2001.

]. A. Ky and . Kytmanov, A transformation formula for Grothendieck residues and some of its applications, Siberian Math. Journal, vol.29, issue.3, pp.495-499, 1989.

S. Lang, Introduction to Arakelov theory, 1988.
DOI : 10.1007/978-1-4612-1031-3

S. Lang and A. , Algèbre linéaire sur K[X 1 , ..., X n ] etéliminationetélimination, Laz] D. Lazard, pp.165-190, 1977.

J. Leray, Le calcul différentiel et intégral sur une variété analytique complexe, Pro-bì eme de Cauchy III, Bull. Soc. Math. France, vol.87, pp.81-180, 1959.

J. Lipman, Residues and Traces of Differential Forms via Hoschschild Homology [Lel] P. Lelong, Plurisubharmonic functions and positive differential forms, Gordon and Breach, Teissier, Clôture intégrale des idéaux etéquisingularitéetéquisingularité, Chapitre I, Publications de l'Institut Fourier, F38402. St. Martin d'H` eres, 1968.

J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math, J, vol.28, pp.199-222, 1981.

J. Lipman and B. Teissier, Pseudo-rational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math, J, vol.28, pp.97-116, 1981.

F. Macaulay, The algebraic theory of modular forms, Matsumura, Commutative algebra, Mathematics Lecture Note Series xv+313 pp. [MM] E. Mayr et A. Meyer, the complexity of the word problem for commutative semigroups and polynomial ideals, pp.305-329, 1916.

M. Méo, Résidus dans le cas non nécessairement intersectioncompì ete, C. R. Acad

M. Méo, Courants r??sidus et formule de King, Arkiv f??r Matematik, vol.44, issue.1, pp.149-165, 2006.
DOI : 10.1007/s11512-005-0003-4

. D. Mw, G. Masser, and . Wüstholz, Fields of large transcendence degree generated by values of elliptic functions, Inventiones math, pp.407-464, 1983.

]. D. North, . G. Northcottnr-]-d, D. Northcott, and . Rees, Lessons on rings, modules and multiplicities Reductions of ideals in local rings, Camb, Phil. Soc, pp.50-145, 1954.

M. Passare, Residues, currents, and their relation to ideals of holomorphic functions., MATHEMATICA SCANDINAVICA, vol.62, issue.1, pp.75-152, 1988.
DOI : 10.7146/math.scand.a-12211

H. Poincaré, Sur les r??sidus des int??grales doubles, Acta Mathematica, vol.9, issue.0, pp.321-380, 1887.
DOI : 10.1007/BF02406742

M. Passare, A. Tsikh, and A. Yger, Residue currents of the Bochner-Martinelli type, Publicacions Matem??tiques, vol.44, pp.85-117, 2000.
DOI : 10.5565/PUBLMAT_44100_02

C. Soulé-(-with, D. Abramovich, J. F. Burnol, J. Kramersa, and ]. Sard, Lectures an Arakelov Theory The measure of the critical values of differentiable maps, Bull. Ann. Math. Soc, pp.48-883, 1942.

C. Sabbah and I. Proximitéproximitéévanescente, Equations fonctionelles pour plusieurs fonctions analytiques, Compositio Math, vol.64, pp.213-241

]. K. Sai and . Saito, Theory of logarithmic differential forms and logarithmic vector fields, J. Fac. Sci. Univ. Tokyo, ser. IA, issue.2, pp.27-265, 1980.

]. J. Se, A. Serre, C. Multiplicités, . Aucolì-ege-de-france, ]. J. Sem et al., Introduction to Algebraic Geometry, 1949.

]. A. Shty, A. Shchuplev, A. Tsikh, and . Yger, Residual kernels with singularities on coordinate planes, Proceedings of the Steklov Institute, pp.256-274, 2006.

]. Y. Siu and . Siu, Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Inventiones math, pp.53-156, 1974.

]. K. Smith and . Smith, An introduction to tight closure, in Geometric and combinatorial aspects of commutative algebra, Lecture Notes in Pure and Appl. Math, vol.217, pp.353-377, 1999.

W. Stoll, The growth of the area of a transcendental analytic set. II, Mathematische Annalen, vol.81, issue.2, pp.144-170, 1964.
DOI : 10.1007/BF01359928

B. Teissier, CyclesévanescentsCyclesévanescents, sections planes et conditions de Whitney, Singularités Singularitésà Cargèse (Rencontre Singularités Géom, Anal., Inst. Etudes Sci., Cargèse, pp.285-362, 1972.

B. Teissier, Varietes polaires II Multiplicites polaires, sections planes, et conditions de whitney, Lecture Notes in Math, vol.77, issue.4, pp.314-491, 1981.
DOI : 10.1007/978-3-662-29244-0

B. Teissier, Monômes, volumes et multiplicités, IntroductionàIntroductionà la théorie des singularités , II, Travaux en Cours, vol.37, pp.127-141, 1988.

P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math, vol.62, pp.177-191, 1995.

]. B. Vdw, . Van-der-waerden, . Algebra, and . Springer-verlag, [VY1] A. Vidras, A. Yger, On asymptotic approximation of the residual currents, Trans. Amer. Math. Soc, vol.350, issue.10, pp.4105-4125, 1959.

A. Vidras and A. Yger, On some generalizations of Jacobi's residue formula, Annales Scientifiques de l?????cole Normale Sup??rieure, vol.34, issue.1, pp.131-157, 2001.
DOI : 10.1016/S0012-9593(00)01056-9

]. A. Weil and . Weil, L???int??grale de Cauchy et les fonctions de plusieurs variables, Math. Ann, vol.111, pp.178-182, 1935.
DOI : 10.1007/978-1-4757-1705-1_16

]. D. Wi and . Widder, The Laplace transform, Analyse complexe et distributions, 1941.

A. Yger, IntroductionàIntroductionà la géométrie analytique complexe etàetà ses applications en arithmétique, 1991.

A. Yger, Courants résidus et Applications, 1994.

A. Yger, Aspects opérationnels de la théorie des résidus hors du cadre intersection compì ete, Géométrie Complexe II, pp.182-204, 2004.

A. Yger, Analytic and algebraic ideas : how to profit from their complementarity, in Harmonic analysis, signal processing, and complexity, Progr. Math, vol.238, pp.15-28, 2005.

A. Yger and U. De, résidu " depuis Poincaré, in L'héritage scientifique d'Henri Poincaré, Editions Echelles The diversity in mathematics respect to a problem in logics On the computation of the complete sum of residues relative to a polynomial mapping in C n, Dokl. Akad. Nauk, vol.275, pp.817-820, 1984.

]. H. Zh1 and . Zhang, Calculs de résidus toriques, C. R. Acad. Sci. Paris Sér. I Math, vol.327, issue.7, pp.639-644, 1998.

H. Zhang, Un syst??me de r??sultants pour tester la propret?? d'une application polynomiale, Colloquium Mathematicum, vol.99, issue.1, pp.19-40, 2004.
DOI : 10.4064/cm99-1-3

H. Zhang, Formules de Jacobi et m??thodes analytiques, Colloquium Mathematicum, vol.102, issue.2, pp.229-243, 2005.
DOI : 10.4064/cm102-2-5