Skip to main content
Log in

Newton polyhedra and the degree of theL-function associated to an exponential sum

  • Published:
Inventiones mathematicae Aims and scope

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Adolphson, A., Sperber, S.: On the degree of theL-function associated with an exponential sum. (to appear)

  2. Bombieri, E.: On exponential sums in finite fields. Am. J. Math.88, 71–105 (1966)

    Google Scholar 

  3. Bombieri, E.: On exponential sums in finite fields, II. Invent. Math.47, 29–39 (1978)

    Google Scholar 

  4. Danilov, V.I.: The geometry of toric varieties. Russ. Math. Surv.33(2), 97–154 (1979)

    Google Scholar 

  5. Deligne, P.: Théorèmes d'intégralité. In: Deligne, P., Katz, N. (eds.), Groupes de monodromie en géométrie algébrique (SGA 7 II). Lect. Notes Math. vol. 340, pp. 384–400. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  6. Deligne, P.: La conjecture de Weil I. Publ. Math. Inst. Hautes Etud. Sci.43, 273–307 (1974)

    Google Scholar 

  7. Deligne, P.: Applications de la formule des traces aux sommes trigonométriques. In: Deligne, P. (ed.) Cohomologie Etale (SGA 4 1/2). Lect. Notes Math., vol.569, pp. 168–232. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  8. Dwork, B.: On the zeta function of a hypersurface. Publ. Math. Inst. Hautes Etud. Sci.12, 5–68 (1962)

    Google Scholar 

  9. Dwork, B.: On the zeta function of a hypersurface, II. Ann. Math.80, 227–299 (1964)

    Google Scholar 

  10. Ehrhart, E.: Sur un problème de géométrie diophantienne linéare, I: Polyèdres et réseaux. J. Reine Angew. Math.226, 1–29 (1967)

    Google Scholar 

  11. Ehrhart, E.: Démonstration de la loi de réciprocité du polyèdre rationnel. C.R. Acad. Sci. Paris Sér. A-B265, A91-A94 (1967)

    Google Scholar 

  12. Kouchnirenko, A.G.: Polyèdres de Newton et nombres de Milnor. Invent. Math.32, 1–31 (1976)

    Google Scholar 

  13. Serre, J-P.: Endomorphismes complètement continus des espaces de Banachp-adiques. Publ. Math. Inst. Hautes Etud. Sci.12, 69–85 (1962)

    Google Scholar 

  14. Sperber, S.:p-Adic hypergeometric functions and their cohomology I. Duke Math. J.44, 535–589 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by NFS Grant N. DMS-8301723.

Partially supported by NFS Grant N. DMS-8301453.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Adolphson, A., Sperber, S. Newton polyhedra and the degree of theL-function associated to an exponential sum. Invent Math 88, 555–569 (1987). https://doi.org/10.1007/BF01391831

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01391831

Keywords

Navigation