Article PDF
Avoid common mistakes on your manuscript.
References
Atiyah, M.F.: Resolution of singularities and division of distributions. Comm. pure Appl. Math.23, 145–150 (1970)
Ax, J., Kochen, S.: Diophantine problems over local fields I, II. Amer. J. Math.87, 605–648 (1965); III. Ann. Math. (2)83, 437–456 (1966)
Bernstein, I.N.: The analytic continuation of generalized functions with respect to a parameter. Functional Anal. Appl.6, 273–285 (1972)
Bernstein, I.N., Gel'fand, S.I.: Meromorphic property of the functionsP λ. Functional Anal. Appl.3, 68–69 (1969)
Bollaerts, D.: On the Poincaré series associated to thep-adic points on a curve (Preprint)
Borewicz, S.E., Šafarevič, I.R.: Zahlentheorie. Basel, Stuttgart: Birkhaeuser 1966
Cohen, P.J.: Decision procedures for real andp-adic fields. Comm. Pure Appl. Math.22, 131–151 (1969)
Delon, F.: Hensel fields in equal characteristicp>0, in Model Theory of Algebra and Arithmetic. Lecture Notes in Mathematics, vol. 834, pp. 108–116, Berlin-Heidelberg-New York: Springer 1980
Driggs, J.H.: Approximations to solutions over Henselian rings. Thesis, Ann Arbor (1976)
Eršov, Ju. L.: On elementary theories of local fields. Algebra i Logika4, 5–30 (1965)
Eršov, Ju.L.: On the elementary theory of maximal normed fields. Soviet Math. Dokl.6, 1390–1393 (1965)
Greenberg, M.J.: Rational points in henselian discrete valuation rings. Publ. Math. IHES31, 59–64 (1966)
Hayes, D.R., Nutt, M.D.: Reflective functions onp-adic fields. Acta Arithmetica XL, 229–248 (1982)
Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. Math.79, 109–326 (1964)
Igusa, J.-I.: Complex powers and asymptotic expansions I. J. reine angew. Math.268/269, 110–130 (1974); II ibid. Igusa, J.-I.: Complex powers and asymptotic expansions I. J. reine angew. Math. 278/279, 307–321 (1975)
Igusa, J.-I.: Some observations on higher degree characters. Am. J. Math.99, 393–417 (1977)
Igusa, J.-I.: On the first terms of certain asymptotic expansions. Complex Analysis and Algebraic Geometry, Baily, W.L., Jr., Shioda, T. (ed.), pp. 357–368. Cambridge University Press, 1977
Igusa, J.-I.: Lectures on forms of higher degree. Tata Inst. Fund. Research, Bombay (1978)
Kiefe, C.: Sets definable over finite fields, their Zeta-Functions. Trans. Amer. Math. Soc.223, 45–59 (1976)
Kochen, S.: The model theory of local fields, in Logic Conference, Kiel 1974. Lecture Notes in Mathematics, vol. 499. Berlin-Heidelberg-New York: Springer 1975
Macintyre, A.: On definable subsets ofp-adic fields. J. Symb. Logic41, 605–610 (1976)
Meuser, D.: On the rationality of certain generating functions. Math. Ann.256, 303–310 (1981)
Meuser, D.: On the poles of a local Zeta function for curves. Invent. Math.73, 445–465 (1983)
Oesterlé, J.: Réduction modulop n des sous-ensembles analytiques fermés de ℤ N p . Invent. math.66, 325–341 (1982)
Oesterlé, J.: Images modulop n d'un sous-ensemble analytique fermé de ℤ N p (Résumé de l'exposé oral). Séminaire de Théorie des Nombres, Paris 1982–83
Prestel, A., Roquette, P.: Lectures on formallyp-adic fields. Lecture Notes in Mathematics, vol. 1050. Berlin-Heidelberg-New York: Springer 1984
Schappacher, N.: Some remarks on a theorem of Greenberg, in Proceedings of the 1979 Kingston Number Theory Conference. Queen's Mathematical Papers, 100–114 (1980)
Serre, J.-P.: Quelques applications du théorème de densité de Chebotarev. Publ. Math. IHES54 (1981)
Strauss, L.: Poles of a two-variablep-adic complex power. Trans. Amer. Math. Soc.278, 481–493 (1983)
Dries, L., van den: Algebraic theories with definable Skolem functions (Preprint)
Weispfenning, V.: On the elementary theory of Hensel Fields. Annals of Math. Logic10, 59–93 (1976)
Weispfenning, V.: Quantifier elimination and decision procedures for valued fields, in Logic Colloquium, Aachen 1983. Lecture Notes in Mathematics (to appear)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Denef, J. The rationality of the Poincaré series associated to thep-adic points on a variety. Invent Math 77, 1–23 (1984). https://doi.org/10.1007/BF01389133
Issue Date:
DOI: https://doi.org/10.1007/BF01389133