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• Weil_conjectures abstract "In mathematics, the Weil conjectures were some highly influential proposals by André Weil (1949) on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with qk elements containing that field. The generating function has coefficients derived from the numbers Nk of points over the (essentially unique) field with qk elements.Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis.The rationality was proved by Dwork (1960), the functional equation by Grothendieck (1965), and the analogue of the Riemann hypothesis was proved by Deligne (1974).".
• Weil_conjectures wikiPageExternalLink grothendieckcircle.org.
• Weil_conjectures wikiPageExternalLink 21.
• Weil_conjectures wikiPageExternalLink item?id=SB_1964-1966__9__41_0.
• Weil_conjectures wikiPageExternalLink index.html.
• Weil_conjectures wikiPageExternalLink 1214437492.
• Weil_conjectures wikiPageExternalLink home.html.
• Weil_conjectures wikiPageExternalLink ~nmk.
• Weil_conjectures wikiPageExternalLink item?id=PMIHES_1974__43__273_0.
• Weil_conjectures wikiPageExternalLink item?id=PMIHES_1980__52__137_0.
• Weil_conjectures wikiPageExternalLink item?id=PMIHES_1987__65__131_0.
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• Weil_conjectures wikiPageExternalLink item?id=SB_1972-1973__15__98_0.
• Weil_conjectures wikiPageID "244705".
• Weil_conjectures wikiPageLength "37420".
• Weil_conjectures wikiPageOutDegree "101".
• Weil_conjectures wikiPageRevisionID "708149187".
• Weil_conjectures wikiPageWikiLink Alexander_Grothendieck.
• Weil_conjectures wikiPageWikiLink Algebraic_curve.
• Weil_conjectures wikiPageWikiLink Algebraic_geometry.
• Weil_conjectures wikiPageWikiLink Algebraic_topology.
• Weil_conjectures wikiPageWikiLink Algebraic_variety.
• Weil_conjectures wikiPageWikiLink American_Journal_of_Mathematics.
• Weil_conjectures wikiPageWikiLink Analytic_number_theory.
• Weil_conjectures wikiPageWikiLink Annals_of_Mathematics.
• Weil_conjectures wikiPageWikiLink Betti_number.
• Weil_conjectures wikiPageWikiLink Blowing_up.
• Weil_conjectures wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
• Weil_conjectures wikiPageWikiLink Cambridge_University_Press.
• Weil_conjectures wikiPageWikiLink Carl_Friedrich_Gauss.
• Weil_conjectures wikiPageWikiLink Category:Conjectures.
• Weil_conjectures wikiPageWikiLink Category:Finite_fields.
• Weil_conjectures wikiPageWikiLink Category:Fixed_points_(mathematics).
• Weil_conjectures wikiPageWikiLink Category:History_of_mathematics.
• Weil_conjectures wikiPageWikiLink Category:Homological_algebra.
• Weil_conjectures wikiPageWikiLink Category:Theorems_in_number_theory.
• Weil_conjectures wikiPageWikiLink Category:Topological_methods_of_algebraic_geometry.
• Weil_conjectures wikiPageWikiLink Category:Zeta_and_L-functions.
• Weil_conjectures wikiPageWikiLink Cohomology.
• Weil_conjectures wikiPageWikiLink Complex_projective_space.
• Weil_conjectures wikiPageWikiLink Cubic_field.
• Weil_conjectures wikiPageWikiLink Cup_product.
• Weil_conjectures wikiPageWikiLink Cyclic_group.
• Weil_conjectures wikiPageWikiLink Disquisitiones_Arithmeticae.
• Weil_conjectures wikiPageWikiLink Elliptic_curve.
• Weil_conjectures wikiPageWikiLink Euler_characteristic.
• Weil_conjectures wikiPageWikiLink Exponential_sum.
• Weil_conjectures wikiPageWikiLink Finite_field.
• Weil_conjectures wikiPageWikiLink Fourier–Deligne_transform.
• Weil_conjectures wikiPageWikiLink Frobenius_endomorphism.
• Weil_conjectures wikiPageWikiLink Functional_equation.
• Weil_conjectures wikiPageWikiLink Galois_module.
• Weil_conjectures wikiPageWikiLink Gauss_sum.
• Weil_conjectures wikiPageWikiLink Gaussian_period.
• Weil_conjectures wikiPageWikiLink Generating_function.
• Weil_conjectures wikiPageWikiLink Glossary_of_arithmetic_and_Diophantine_geometry.
• Weil_conjectures wikiPageWikiLink Hasses_theorem_on_elliptic_curves.
• Weil_conjectures wikiPageWikiLink Hilbert–Speiser_theorem.
• Weil_conjectures wikiPageWikiLink Inventiones_Mathematicae.
• Weil_conjectures wikiPageWikiLink Jean-Pierre_Serre.
• Weil_conjectures wikiPageWikiLink Kähler_manifold.
• Weil_conjectures wikiPageWikiLink Künneth_theorem.
• Weil_conjectures wikiPageWikiLink Lefschetz_fixed-point_theorem.
• Weil_conjectures wikiPageWikiLink Lefschetz_hyperplane_theorem.
• Weil_conjectures wikiPageWikiLink Lefschetz_pencil.
• Weil_conjectures wikiPageWikiLink Leray_spectral_sequence.
• Weil_conjectures wikiPageWikiLink Local_zeta-function.
• Weil_conjectures wikiPageWikiLink Mathematics.
• Weil_conjectures wikiPageWikiLink Mathematische_Zeitschrift.
• Weil_conjectures wikiPageWikiLink Michael_Artin.
• Weil_conjectures wikiPageWikiLink Morse_theory.
• Weil_conjectures wikiPageWikiLink Number_theory.
• Weil_conjectures wikiPageWikiLink P-adic_number.
• Weil_conjectures wikiPageWikiLink Perverse_sheaf.
• Weil_conjectures wikiPageWikiLink Picard–Lefschetz_theory.
• Weil_conjectures wikiPageWikiLink Poincaré_duality.
• Weil_conjectures wikiPageWikiLink Point_at_infinity.
• Weil_conjectures wikiPageWikiLink Projective_variety.
• Weil_conjectures wikiPageWikiLink Publications_Mathxc3xa9matiques_de_lIHxc3x89S.
• Weil_conjectures wikiPageWikiLink Quaternion_algebra.
• Weil_conjectures wikiPageWikiLink Ramanujan_tau_function.
• Weil_conjectures wikiPageWikiLink Ramanujan–Petersson_conjecture.
• Weil_conjectures wikiPageWikiLink Rational_function.
• Weil_conjectures wikiPageWikiLink Rational_point.
• Weil_conjectures wikiPageWikiLink Riemann_hypothesis.
• Weil_conjectures wikiPageWikiLink Riemann_sphere.
• Weil_conjectures wikiPageWikiLink Riemann_zeta_function.
• Weil_conjectures wikiPageWikiLink Rigid_cohomology.
• Weil_conjectures wikiPageWikiLink Root_of_unity.
• Weil_conjectures wikiPageWikiLink Singular_point_of_an_algebraic_variety.
• Weil_conjectures wikiPageWikiLink Société_mathématique_de_France.
• Weil_conjectures wikiPageWikiLink Springer_Science+Business_Media.
• Weil_conjectures wikiPageWikiLink Standard_conjectures_on_algebraic_cycles.
• Weil_conjectures wikiPageWikiLink Supersingular_elliptic_curve.
• Weil_conjectures wikiPageWikiLink Weil_cohomology_theory.
• Weil_conjectures wikiPageWikiLink Étale_cohomology.
• Weil_conjectures wikiPageWikiLinkText "Riemann hypothesis for zeta-functions".
• Weil_conjectures wikiPageWikiLinkText "Weil conjectures".
• Weil_conjectures authorlink "André Weil".
• Weil_conjectures authorlink "Bernard Dwork".

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