Lectures on zeta functions over finite fields

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Wan, Daqing (2007)
  • Subject: Mathematics - Algebraic Geometry | Mathematics - Number Theory
    arxiv: Mathematics::Number Theory

These are the notes from the summer school in G\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over finite fields, focusing on moment zeta functions and zeta functions of affine toric hypersurfaces.
  • References (32)
    32 references, page 1 of 4

    [1] A. Adolphson and S. Sperber. Exponential sums and Newton polyhedra: Cohomology and estimates. Ann. Math., 130 (1989), 367-406.

    [2] P. Berthelot and A. Ogus, Notes on Crystalline Cohomology, Princeton University Press, 1978.

    [3] P. Candelas, X. de la Ossa, F. Rodriques-Villegas, Calabi-Yau manifolds over finitef fields II, Fields Instit. of Commun., 38(2003).

    [4] J. Denef and F. Loesser, Weights of exponential sums, intersection cohomology, and Newton polyhedra, Invent. Math., 106(1991), no.2, 275-294.

    [5] P. Deligne, Applications de la Formule des Traces aux Sommes Trigonom´etriques, in Cohomologie E´tale (SGA 4 21 ), 168-232, Lecture Notes in Math. 569, Springer-Verlag 1977.

    [6] P. Deligne, La Conjecture de Weil II, Publ. Math. IHES 52 (1980), 137-252.

    [7] B. Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math., 82(1960), 631-648.

    [8] B. Dwork, Normalized period matrices II, Ann. Math., 98(1973), 1-57.

    [9] L. Fu and D. Wan, Moment L-functions, partial L-functions and partial exponential sums, Math. Ann., 328(2004), 193-228.

    [10] L. Fu and D. Wan, L-functions for symmetric products of Kloosterman sums, J. Reine Angew. Math., 589(2005), 79-103.

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