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- Height_zeta_function abstract "In mathematics, the height zeta function of an algebraic variety or more generally a subset of a variety encodes the distribution of points of given height.If S is a set with height function H, such that there are only finitely many elements of bounded height, define a counting functionand a zeta functionIf Z has abscissa of convergence β and there is a constant c such that N has rate of growth then a version of the Wiener–Ikehara theorem holds: Z has a t-fold pole at s = β with residue c.a.Γ(t).The abscissa of convergence has similar formal properties to the Nevanlinna invariant and it is conjectured that they are essentially the same. More precisely, Batyrev–Manin conjectured the following. Let X be a projective variety over a number field K with ample divisor D giving rise to an embedding and height function H, and let U denote a Zariski-open subset of X. Let α = α(D) be the Nevanlinna invariant of D and β the abscissa of convergence of Z(U, H; s). Then for every ε > 0 there is a U such that β < α + ε: in the opposite direction, if α > 0 then α = β for all sufficiently large fields K and sufficiently small U.".
- Height_zeta_function wikiPageID "35800065".
- Height_zeta_function wikiPageRevisionID "505608033".
- Height_zeta_function hasPhotoCollection Height_zeta_function.
- Height_zeta_function subject Category:Diophantine_geometry.
- Height_zeta_function subject Category:Geometry_of_divisors.
- Height_zeta_function comment "In mathematics, the height zeta function of an algebraic variety or more generally a subset of a variety encodes the distribution of points of given height.If S is a set with height function H, such that there are only finitely many elements of bounded height, define a counting functionand a zeta functionIf Z has abscissa of convergence β and there is a constant c such that N has rate of growth then a version of the Wiener–Ikehara theorem holds: Z has a t-fold pole at s = β with residue c.a.Γ(t).The abscissa of convergence has similar formal properties to the Nevanlinna invariant and it is conjectured that they are essentially the same. ".
- Height_zeta_function label "Height zeta function".
- Height_zeta_function sameAs m.0js___4.
- Height_zeta_function sameAs Q5699096.
- Height_zeta_function sameAs Q5699096.
- Height_zeta_function wasDerivedFrom Height_zeta_function?oldid=505608033.
- Height_zeta_function isPrimaryTopicOf Height_zeta_function.