On the zeta function of a hypersurface. I

DOI10.1007/BF02684275zbMath0173.48601OpenAlexW2138978560WikidataQ97011254 ScholiaQ97011254MaRDI QIDQ2532357

Publication date: 1962

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1962__12__5_0

zbMATH Keywords

algebraic geometry

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Arithmetic ground fields for surfaces or higher-dimensional varieties (14J20)

Related Items

Newton polygons for $L$-functions of generalized Kloosterman sums, Unnamed Item, Unnamed Item, Zeta functions of alternate mirror Calabi-Yau families, Geometry of the scaling site, Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations, Unnamed Item, $L$-functions of twisted exponential sums over finite fields, Newton stratification for polynomials: the open stratum, Torsion points on Jacobians of quotients of Fermat curves and $p$-adic soliton theory, Exponential sums and rigid cohomology, Newton polyhedra and the degree of the L-function associated to an exponential sum, NEWTON POLYGONS FOR CHARACTER SUMS AND POINCARÉ SERIES, $L$-functions of twisted diagonal exponential sums over finite fields, On the intersection matrix of a hypersurface, Asymptotic variation of L functions of one-variable exponential sums, Aspects of topological approaches for data science, Logarithmic decay and overconvergence of the unit root and associated zeta functions, On the Jacobian ring of a complete intersection, Rigid cohomology and $p$-adic point counting, On the classification of commutative formal group laws over p-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices, Unnamed Item, $L$-functions of exponential sums and Hasse polynomials, On the Newton Polytope, Distinguished-root formulas for generalized Calabi-Yau hypersurfaces, L-functions of certain exponential sums over finite fields. II, Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$, Some open problems related to creative telescoping, Formulas for roots of $L$-functions of the Airy exponential sums, Generic exponential sums associated with polynomials of degree 3 in two variables, Une introduction naïve aux cohomologies de Dwork, Approximation of continuous and differentiable functions in a locally compact field, Unnamed Item, Improvements to the deformation method for counting points on smooth projective hypersurfaces, On the L-functions associated with certain exponential sums, Exponential sums and Newton polyhedra, Generalizations of the Schrödinger maximal operator: building arithmetic counterexamples, Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology, Newton polygons of L-functions for two-variable generalized Kloosterman sums, Unnamed Item, Algorithms for minimal Picard-Fuchs operators of Feynman integrals, Rational points over finite fields for regular models of algebraic varieties of Hodge type $\geq 1$, Torsion points on hyperelliptic Jacobians via Anderson's $p$-adic soliton theory, Regular decomposition of ordinarity in generic exponential sums, On twisted de Rham cohomology, $p$-adic estimates for exponential sums and the theorem of Chevalley-Warning, On the zeta function of a complete intersection, Point counting in families of hyperelliptic curves, An analogue of the von Staudt-Clausen theorem, Newton polygons of $L$-functions associated to Deligne polynomials, The $L$-functions of Witt coverings, On the characteristic power series of the $U$ operator, On the $L$-function of multiplicative character sums, Hasse polynomials of $L$-functions of certain exponential sums, Newton polygons of $L$ functions associated with exponential sums of polynomials of degree four over finite fields, Exponential sums on $\mathbb{A}^n$., Monodromy and the Tate conjecture: Picard numbers and Mordell-Weil ranks in families., Consequences of a result of N. Katz and G. Laumon concerning trigonometric sums, Variations of the mixed Hodge structure of affine hypersurfaces in algebraic tori, The local Torelli theorem. I: Complete intersections, A lower bound for the number of solutions of equations over finite fields, Computing periods of rational integrals, Arithmetic on algebraic varieties, Exponential sums on 𝐀ⁿ, II, On the zeta function of a projective complete intersection, Hasse-Witt matrices for polynomials, and applications, Berkovich spectra of elements in Banach rings, On the differential equations satisfied by period matrices, Zur Funktionentheorie einer Veränderlichen über einem vollständigen nichtarchimedischen Grundkörper, Exponential sums on $(\mathbb{G}_ m)^ n$, On twisted exponential sums, $A$-hypergeometric series and a $p$-adic refinement of the Hasse-Witt matrix, Computing periods of hypersurfaces, A $p$-adic Serre bound, On Hecke polynomials, L-functions of certain exponential sums over finite fields, Generalization of the von Staudt-Clausen theorem, Computing zeta functions of Artin-Schreier curves over finite fields. II, Completely continuous endomorphisms of $p$-adic Banach spaces, Higher solutions of hypergeometric systems and Dwork cohomology, Abstract algebraic geometry, $p$-adic cycles, Unnamed Item, G-Fonctions et cohomologie des hypersurfaces singuliéres II, Unnamed Item, Maximum principle for analytic elements and Lubin-Hensel's theorem in $H(D)Y$, Familles compactes de fractions rationnelles et ensembles fermés de nombres algébriques, Sous-corps fermés d'un corps valué, Nonarchimedean spectral theory, Hyperkloosterman sums revisited, $L$-functions associated to overconvergent $F$-isocrystals, On a certain poisson formula, Some supercongruences related to truncated hypergeometric series, Newton polygons for $L$-functions of exponential sums of polynomials of degree six over finite fields., Alternating and symmetric multilinear forms and poincaré algebras, Hypergeometric functions and rings generated by monomials

Cites Work