Skip to main content
SpringerLink
Log in

Work of Philippe Robba

  • Chapter
  • First Online:
p-adic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1454))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography of Ph. Robba

  • [1966] “Dérivée en moyenne de fonction moyennable”, Communication an Congrés des Mathematiciens, Moscow, 2p.

    Google Scholar 

  • [1967] “Solutions presque-periodiques d'équations differentielles aux différences”, Seminaire Lions-Schwartz, 25p.

    Google Scholar 

  • [1969a] (with E. Motzkin), “Ensembles satisfaisant au principe du prolongement analytique en analyse p-adique” C.R. Acad. Sc. Paris 269, p. 126–129.

    MathSciNet  MATH  Google Scholar 

  • [1969b] ____, “Ensembles d'analyticité en analyse p-adique”, C.R. Acad. Sc. Paris 269, p. 450–453.

    MathSciNet  MATH  Google Scholar 

  • [1970] “Decomposition en élements simple d'une fonction analytique sur un corps valué ultramétrique. Application au prolongement analytique”, Sem. Delange-Pisot-Poitou, (1969/70), No. 22, 14p.

    Google Scholar 

  • [1971] “Prolongement analytique pour les fonction de plusieurs variables sur un corps valué complet”, Sem. Delange-Pisot-Poitou, (1971/72).

    Google Scholar 

  • [1972a] “Decomposition en élements simple d'un elément analytique sur un corps ultramétrique”, C.R. Acad. Sc. Paris 274, p. 532–535.

    MathSciNet  MATH  Google Scholar 

  • [1972b] “Fonctions analytiques sur un corps ultramétrique”, C.R. Acad. Sc. Paris 274, p. 721–723.

    MathSciNet  MATH  Google Scholar 

  • [1972c] “Prolongement analytique en analyse ultramétrique”, C.R. Acad. Sci. Paris 274, p. 830–833.

    MathSciNet  MATH  Google Scholar 

  • [1973a] “Fonctions analytiques sur les corps valués ultramétriques complets”, Asterisque, 10, p. 109–220.

    MathSciNet  MATH  Google Scholar 

  • [1973b] “Prolongement analytique pour les fonctions de plusieurs variables sur un corps valué complet”, Bull. Soc. Math. France 101, pp. 193–217.

    MathSciNet  MATH  Google Scholar 

  • [1974a] “Croissance des solutions d'une équation differentille homogéne”, GEAU 73/74, exp. 1, 15p.

    Google Scholar 

  • [1974b] “Indice d'un opérateur différentiel”, GEAU 73/74, exp. 2, 14p.

    Google Scholar 

  • [1974c] “Prolongement des solutions d'un équation différentielle p-adique”, GEAU 73/74 exp 11, 3p. (also C.R. Acad. Sc. 279, p. 153–154).

    Google Scholar 

  • [1974d] “Quelques propriétes des éléments et fonctions analytiques au sens de Krasner”, Bull. Soc. Math. France Mémoire 39–40, p. 341–349.

    Google Scholar 

  • [1974e] “Un classe d'ensembles analytiques á plusieurs dimensions”, Bull. Soc. Math France, Mémoire 39–40, p. 351–357.

    Google Scholar 

  • [1975a] “On the index of p-adic differential operators I”, Annals of Math. 101 p. 280–316.

    Article  MathSciNet  MATH  Google Scholar 

  • [1975b] “Equations différentielles p-adiques”, Sem. Delange-Pisot-Pitou, 74/75, 15p.

    Google Scholar 

  • [1975c] “Factorisation d'un opérateur différentiel”, GEAU 74/75 exp. 2, 16p.

    Google Scholar 

  • [1975d] “Factorisation d'un opérateur diffèrentiel”, Applications, GEAU 74/75 exp. 10, 6p.

    Google Scholar 

  • [1975e] “Caracterisation des dérivées logarithmiques”, GEAU 74/75 exp. 12, 6p.

    Google Scholar 

  • [1975f] “Lemma de Hensel pour les opérateurs différentielles” GEAU 74/75 exp. 16, 11p.

    Google Scholar 

  • [1975g] “Structure de Frobenius faible pour les équations différentielles de premier ordre”, GEAU 74/75 exp. 20, 11p.

    Google Scholar 

  • [1976a] “On the index of p-adic differential operators II”, Duke Math. J. 43, p. 19–31.

    Article  MathSciNet  MATH  Google Scholar 

  • [1976b] “Solutions bornées des systems différentiels linéaires, Application aux fonctions hypergéométriques”, GEAU 75/76 exp. 5, 16p.

    Google Scholar 

  • [1976c] “Factorisation d'un opérateur différentiel II”, GEAU 75/76 exp. 6, 6p.

    Google Scholar 

  • [1976d] “Prolongement algébrique et equations différentielles”, Proc. Conference on p-adic analysis, Nijmegen (1978), p. 172–184. Math. Inst. Katholieke Univ. Toernooiveld.

    Google Scholar 

  • [1976e] “Théorie de Galois p-adique”, GEAU 75/76 exp. 14, 8p.

    Google Scholar 

  • [1976f] “Lemme de Schwarz p-adique pour plusieurs variables” GEAU 75/76 exp. J9, 12p.

    Google Scholar 

  • [1977a] (with B. Dwork) “On ordinary linear p-adic differential equations”, Trans. Amer. Math. Soc. 231, p. 1–46.

    MathSciNet  MATH  Google Scholar 

  • [1977b] “Nouveau point de vue sur le prolongement algébrique”, GEAU 76/77 exp. 5, 14p.

    Google Scholar 

  • [1977c] “Disque générique et équations différentielles”, GEAU 76/77 exp. 8, 7p.

    Google Scholar 

  • [1977d] “Nombre de zéros des fonctions exponentielles-polynômes”, GEAU 76/77 exp. 9, 3p.

    Google Scholar 

  • [1978a] “Lemmes de Schwarz of lemmes d'approximation p-adiques en plusieurs variables”, Invent. Math. 48, 245–277.

    Article  MathSciNet  MATH  Google Scholar 

  • [1978b] “Zéros de suites récurrentes linéaires”, GEAU 77/78 exp. 13, 5p.

    Google Scholar 

  • [1979a] (with B. Dwork) “On natural radii of p-adic convergence”, Trans. Amer. Math. Soc. 256, p. 199–213.

    MathSciNet  MATH  Google Scholar 

  • [1979b] “Points singuliers d'equations différentielles, d'apres F. Baldassarri”, GEAU 78/79 exp. 5, 2p.

    Google Scholar 

  • [1979c] (with B. Dwork) “Majorations effective”, GEAU 78/79 exp. 18, 2p.

    Google Scholar 

  • [1979d] “Clôture algébrique relative de certain anneaux de séries entières”, GEAU 78/79 exp. 21, 2p.

    Google Scholar 

  • [1979e] “Lemmes de Hensel pour les opérateurs differéntielles”, GEAU 78/79 exp. 23, 8p.

    Google Scholar 

  • [1980a] “Lemmes de Hensel pour les opérateurs différentielles, Application a la reduction formelle des equations différentielles”, Ens. Math. 26, p. 279–311.

    MathSciNet  MATH  Google Scholar 

  • [1980b] (with B. Dwork) “Effective p-adic bounds for solutions of homogeneous linear differential equations”, Trans. Amer. Math. Soc. 259, p. 559–577.

    MathSciNet  MATH  Google Scholar 

  • [1980c] (with S. Bosch and B. Dwork) “Un theorem de prolongement pour les fonctions analytiques”, Math. Ann. 242, p. 165–173.

    MathSciNet  MATH  Google Scholar 

  • [1980d] “Factorisation d'opérateurs différentiel á coefficients rationnels”, GEAU 79/81 exp. 12, 3p.

    Google Scholar 

  • [1981] “Une propriété de specialisation continue, d'après Artin, Bosch, Lang, Van den Dries”, GEAU 79/81 exp. 26, 11p.

    Google Scholar 

  • [1982a] “Sur les equations différentielles linéaires p-adiques II”, Pacific J. Math. 98, p. 393–418.

    Article  MathSciNet  MATH  Google Scholar 

  • [1982b] “Calcul des residus en analyse p-adique, d'apres Gerritzen et Van der Put”, GEAU 81/82 exp. 28, 8p.

    Google Scholar 

  • [1982c] “Indice d'un opérateur différentiel linéaire p-adique d'ordre 1 et cohomologies p-adiques”, GEAU 81/82 exp. J15, 10p.

    Google Scholar 

  • [1983] “Cohomologie de Dwork, I”, GEAU 82/83 exp. 3, 10p.

    Google Scholar 

  • [1984a] “Une Introduction naive aux cohomologies de Dwork”, Bull. Soc. Math. France 114 (Supp) Memoire 23, p. 61–105.

    MathSciNet  MATH  Google Scholar 

  • [1984b] “Index of p-adic differential operators III, Application to twisted exponential sums”, Astérisque, 119–120, p. 191–266.

    MathSciNet  MATH  Google Scholar 

  • [1984c] “Quelques remarques sur les opérateurs différentiels d'order 1”, GEAU 83/84 exp. 12, 8p.

    Google Scholar 

  • [1985a] “Indice d'un opérateur différentiel p-adique IV, Cas des systèms. Mesure d'irregularité dans un disque”, Ann. Inst. Fourier 35, p. 13–35.

    Article  MathSciNet  Google Scholar 

  • [1985b] “Conjecture sur les equations différentielles p-adiques linéaires”, GEAU exp. 2, 8p.

    Google Scholar 

  • [1985c] “Product symmetrique de l'equation de Bessel”, GEAU exp. 7, 3p.

    Google Scholar 

  • [1986a] “Symmetric powers of the p-adic Bessel Function”, Crelle 366, p. 194–220.

    MathSciNet  MATH  Google Scholar 

  • [1986b] (with J. P. Bezivin) “Rational solutions of linear differential equations”, Proc. of conference on p-adic analysis, Hengelhoef, Belg. p. 11–18.

    Google Scholar 

  • [1987] “Propriete d'approximation pour les elements algébriques”, Comp. Math. 63, p. 3–14.

    MathSciNet  MATH  Google Scholar 

  • [1989a] (with J. P. Bezivin) “A new p-adic method for proving irrationality and transcendence results”, Ann. of Math. 129, p. 151–160.

    Article  MathSciNet  MATH  Google Scholar 

  • [1989b] “Rational solutions of linear differential equations”, J. Australian Math. Soc. 46, p. 184–196.

    Article  MathSciNet  MATH  Google Scholar 

General Bibliography

  • [1976a] Adolphson, A., “An index theorem for p-adic differential operators”, Trans. Amer. Math. Soc. 216, 279–293.

    MathSciNet  MATH  Google Scholar 

  • [1976b] ____, “A p-adic theory of Hecke polynomials”, Duke Math. J. 43, 115–145.

    Article  MathSciNet  MATH  Google Scholar 

  • [1982] ____, Dwork, B., Sperber, S., “Growth of solutions of linear differential equations at a logarithmic singularity”, Trans. Amer. Math. Soc. 271, 245–252.

    Article  MathSciNet  MATH  Google Scholar 

  • [1984] ____, Sperber, S., “Twisted kloosterman sums and p-adic Bessel functions”, Amer. J. Math. 105, 549–591.

    Article  MathSciNet  MATH  Google Scholar 

  • [1981] Christol, “Systémes différentiels linéaires p-adiques”, Structure de Frobenius Faible, Bull. Soc. Math. France 109, 83–122.

    MathSciNet  MATH  Google Scholar 

  • [1984] ____, “Un theorem de transfert pour les disques singuliers réguliers”, Astérisque 119–120, 151–168.

    MathSciNet  MATH  Google Scholar 

  • [1990 ____, Dwork, B. “Effective p-adic bounds at regular singular points”, Duke Math. J. (submitted).

    Google Scholar 

  • [1966] Clark, D. “A note on the p-adic convergence of solutions of linear differential equations”, Proc. Amer. Math. Soc. 17, 262–269.

    MathSciNet  MATH  Google Scholar 

  • [1964] Dwork, B. “On the zeta function of a hypersurface II”, Ann. Math. 80, 227–299.

    Article  MathSciNet  Google Scholar 

  • [1966] ____, “On the zeta function of a hypersurface III”, Ann. Math. 83, 457–519.

    Article  MathSciNet  Google Scholar 

  • [1969] ____, “p-adic cycles”, Pub. Math. IHES 37, 27–116.

    Article  MathSciNet  MATH  Google Scholar 

  • [1971] ____, “Normalized period matrices I”, Ann. Math. 93, 337–388.

    Article  MathSciNet  MATH  Google Scholar 

  • [1973] ____, “Normalized period matrices II”, Ann. Math. 98, 1–57.

    Article  MathSciNet  MATH  Google Scholar 

  • [1982] ____, Lectures on p-adic differential equations, Springer-Verlag.

    Google Scholar 

  • [1987] ____, “On the Tate constant”, Comp. Math. 61, 43–59.

    MathSciNet  MATH  Google Scholar 

  • [1990] ____, Sperber, S., “Logarithmic decay and over convergence of the unit root and associated zeta functions”, Ann. Sc. ENS, to appear.

    Google Scholar 

  • [1973] Katz, N., Travaux de Dwork, Sem. Bourbuki 71/72 exp. 409 (Lecture Notes in Math., Springer-Verlag).

    Google Scholar 

  • [1937] Lutz, E., “Sur l'equation y 2 = x 3 − Ax − B dans les corps p-adiques”, J. Reine Angew. Math. 177, 238–247.

    MathSciNet  MATH  Google Scholar 

  • [1981] Sibuya, Y., Sperber, S., “Arithmetic properties of power series solutions of algebraic differential equations”, Ann. Math. 113, 111–157.

    Article  MathSciNet  MATH  Google Scholar 

  • [1985] ____, On the p-adic continuation of the logarithmic derivative of certain hypergeometric functions, GEAU 84/85 exp. 4, 5p.

    Google Scholar 

  • [1980] Sperber, S., “Congruence properties of the hyperkloosterman sum”, Comp. Math. 40, 3–32.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Princeton University, USA

    B. Dwork

Authors
  1. B. Dwork
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Francesco Baldassarri Siegfried Bosch Bernard Dwork

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Dwork, B. (1990). Work of Philippe Robba. In: Baldassarri, F., Bosch, S., Dwork, B. (eds) p-adic Analysis. Lecture Notes in Mathematics, vol 1454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091131

Download citation

  • DOI: https://doi.org/10.1007/BFb0091131

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53477-8

  • Online ISBN: 978-3-540-46906-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation