Geodesic
Periods and the Asymptotics of a Diophantine Problem II
Canadian journal of mathematics, Tome 43 (1991) no. 4, pp. 770-791

Voir la notice de l'article provenant de la source Cambridge University Press

Let P(z 1,..., z n ) be a polynomial with positive coefficients. For positive x define A classical diophantine problem is to describe the asymptotic behavior of N 1(x) as x → ∞. More generally, one can introduce a second polynomial φ satisfying the condition (0.1) Sign φ (m) is constant for all m outside at most a finite subset of Nn . 
Lichtin, Ben. Periods and the Asymptotics of a Diophantine Problem II. Canadian journal of mathematics, Tome 43 (1991) no. 4, pp. 770-791. doi: 10.4153/CJM-1991-044-9
@article{10_4153_CJM_1991_044_9,
     author = {Lichtin, Ben},
     title = {Periods and the {Asymptotics} of a {Diophantine} {Problem} {II}},
     journal = {Canadian journal of mathematics},
     pages = {770--791},
     year = {1991},
     volume = {43},
     number = {4},
     doi = {10.4153/CJM-1991-044-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-044-9/}
}
TY  - JOUR
AU  - Lichtin, Ben
TI  - Periods and the Asymptotics of a Diophantine Problem II
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 770
EP  - 791
VL  - 43
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-044-9/
DO  - 10.4153/CJM-1991-044-9
ID  - 10_4153_CJM_1991_044_9
ER  - 
%0 Journal Article
%A Lichtin, Ben
%T Periods and the Asymptotics of a Diophantine Problem II
%J Canadian journal of mathematics
%D 1991
%P 770-791
%V 43
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-044-9/
%R 10.4153/CJM-1991-044-9
%F 10_4153_CJM_1991_044_9

[Be] Bernstein, J.N., The analytic continuation of generalized functions with respect to a parameter, Functional Analysis and Applications. 6(1972), 26–40. Google Scholar

[Bro-1] Broughton, S.A., On the topology of polynomial hyper surfaces, Proc. of Symp. in Pure Math. 40 part 1 (1983), 167–178. Google Scholar

[Bro-2] Broughton, S.A.,Milnor numbers and the topology of polynomial hypersurfaces,Inv. Math. 92(1988), 217–241. Google Scholar

[Bro-3] Broughton, S.A., On the topology of polynomial hypersurfaces. Thesis at Queen's University, 1982. Google Scholar

[C-N] Cassou-Nogues, P., Valeurs aux entiers négatifs des series de Dirichlet associées à un polynome II, Amer. J. Math. 106(1985), 255–299. Google Scholar

[Da-Kh] Danilov, V. I. and Khovanski, A.G., Newton polyhedra and an algorithm for computing Hodge- Deligne numbers, Math. USSR Izves. 29(1987), 279–299. Google Scholar

[Dav] Davenport, H., Analytic methods for diophantine equations and diophantine inequalities. University of Michigan lecture notes, 1962. Google Scholar

[De] Deligne, P., Equations différentielles à Points Singuliers Réguliers. Lecture Notes in Mathematics 163, Springer-Verlag, 1970. Google Scholar

[Gin] Gindikin, S.G., Energy estimates involving the Newton polyhedron,Trans, . Moscow Math. Soc. 31(1974), 193–245. Google Scholar

[Gr] Griffithsom, P.A. results on moduli and periods of integrals on algebraic manifolds. Mimeographed Princeton U. notes, 1968. Google Scholar

[He] Herrera, M., Integration on a semi-analytic set, Bull. Soc. Math. France 94(1966), 141–180. Google Scholar

[Hoo]Hooley, C.,Orc Waring's Problem, ActaMathematica 157(1986),49–97. Google Scholar

[Ku] Kushinirenko, A., Polyèdres de Newton et nombres de Milnor, Inv. Math. 32(1976), 1–32. Google Scholar

[Li-1] Lichtin, B., GeneralizedDirichlet series and B-functions, Compositio Math. 65(1988), 81–120. Google Scholar

[Li-2] Lichtin, B., Periods and the asymptotics of a diophantine Problem, (to appear in Arkiv fur Mathematik). Google Scholar

[Li-3] Lichtin, B., The asymptotics of a lattice point problem determined by a hypoelliptic polynomial, (to appear). Google Scholar

[Lo] Lojasiewicz, S., Triangulation of semi-analytic sets, Ann. Scuola Normale sup. de Pisa 3rd series, 18 (1964), 449–474. Google Scholar

[Ma-1] Malgrange, B., Intégrales asymptotiques et monodromie, Ann. Scient. Ec. Norm. Sup. 7(1974), 405–430. Google Scholar

[Ma-2] Malgrange, B. ,Méthode de la phase stationnaire et sommation de Borel, Complex Analysis, Microlocal Calculus, and Relativistic Quantum Field Theory, Lecture Notes in Physics, Springer-Verlag 126, 1980. Google Scholar

[Nil] Nilsson, N., Some growth and ramification properties of certain integrals on algebraic manifolds, Arkiv fur Mathematik 5(1965), 463–475. Google Scholar

[P-l] Pham, F., Vanishing homologies and the n-variable saddlepoint method, Proc. Symp. in Pure Math 40, part 2 (1983), 319–334. Google Scholar

[P-2] Pham, F. ,La descente des cols par les onglets de Lefschetz avec vues sur Gauss-Manin, Astérisque 130(1985), 11–47. Google Scholar

[Sa-1] Sargos, P., Prolongement meromorphe des séries de Dirichlet associées a des fractions rationelles de plusieurs variables, Ann. Inst. Fourier 33(1984), 82–123. Google Scholar

[Sa-2] Sargos, P.,Croissance de certaines séries de Dirichlet et applications, J. fur die reine und angewandte Mathematik 367(1986), 139–154. Google Scholar

[Sa-3] Sargos, P., Series de Dirichlet et polyèdres de Newton. These d'Etat, Université de Bordeaux, 1986. Google Scholar

[Spa] Spanier, E., Algebraic Topology. McGraw-Hill, 1966. Google Scholar

[Va] Vaughn, R.C., The Hardy-Littlewood Method. Cambridge Univ. Press, 1981. Google Scholar

[Var] Varcenko, A.N., Zeta function of monodromy and Newton diagrams, Inv. Math. 37(1976), 253–262. Google Scholar

[Ve] Verdier, J.-L., Stratifications de Whitney et Théorème de Bertini-Sard, Inv. Math. 36(1976), 295–312. Google Scholar

Cité par Sources :