mathematics, the Hasse–Weil zeta function attached to an algebraic variety V defined over an algebraic number field K is a meromorphic function on the complex...

field Hasse–Weil zeta function of a variety Height zeta function of a variety Hurwitz zeta function, a generalization of the Riemann zeta function Igusa...

number theory, the local zeta function Z(V, s) (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as Z ( V , s...

the Artin conjecture for L-functions. Additionally, ζK(s) is the Hasse–Weil zeta function of Spec OK and the motivic L-function of the motive coming from...

agree with the corresponding factor of the Hasse–Weil zeta function of XQ. Therefore, these two functions are closely related. There are a number of conjectures...

Scientifiques/Collected Papers by André Weil ISBN 0-387-90330-5 Dwork, Bernard (1960), "On the rationality of the zeta function of an algebraic variety", American...

zeta-functions, arising at a fundamental level for the (analogue of) Poincaré duality in étale cohomology. The Euler products of the Hasse–Weil zeta-function...

clearer in what sense the construction of Hasse–Weil zeta functions might be made to work to provide valid L-functions, in the analytic sense: there should...

function has coefficients derived from the numbers Nk of points over the extension field with qk elements. Weil conjectured that such zeta functions for...

fixed-point theorem in algebraic topology, used to express the Hasse–Weil zeta function. Gutzwiller trace formula: See Quantum chaos Kuznetsov trace formula...

Unsolved problem in mathematics: Do all non-trivial zeroes of the Riemann zeta function have a real part of one half? (more unsolved problems in mathematics)...

theorem Euler system p-adic L-function Arithmetic geometry Complex multiplication Abelian variety of CM-type Chowla–Selberg formula Hasse–Weil zeta function...

ingredient is a function of a complex variable, L, the Hasse–Weil zeta function of E over Q. This function is a variant of the Riemann zeta function and Dirichlet...

the local zeta-function of C, and is the analogue of the Riemann hypothesis for the function field associated with the curve. The Hasse–Weil bound reduces...

polynomial of the Frobenius endomorphism. As a consequence, the Hasse–Weil zeta function for E is a product of two Dirichlet series, for χ and its complex...

congruence relation, implies that the Hasse–Weil zeta function of a modular curve is a product of L-functions associated to explicitly determined modular...

geometry (Hasse principle), and to local zeta functions. Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written...

than the invariants, but the result here will be the same. Cf. Hasse–Weil L-function for a similar situation. Perlis 2001. Martinet 1977, p. 18. Prasad...

powers in one variable. Lars Hesselholt (2016) showed that the Hasse–Weil zeta function of a smooth proper variety over F p {\displaystyle \mathbb {F}...

theorem Weil's explicit formula Hasse-Weil bound Hasse–Weil zeta function, and the related Hasse–Weil L-function Mordell–Weil group Mordell–Weil theorem...

pivotal role in the Langlands program, by identifying a part of the Hasse–Weil zeta function of a modular curve or a more general modular variety, with the...

an algebraic group, proved by Kottwitz and others. The Hasse–Weil conjecture about zeta functions. This disambiguation page lists mathematics articles associated...

ISBN 978-3-540-61018-2. Weil, A. (1938). "Zur algebraischen Theorie der algebraischen Funktionen. (Aus einem Brief an H. Hasse.)". Journal für die reine...

coefficients a n {\displaystyle a_{n}} are defined in Hasse–Weil zeta function. The generating function of the coefficients a n {\displaystyle a_{n}} is then...

in which the Hasse–Weil zeta functions of arithmetic quotients of the upper half plane are identified with L {\displaystyle L} -functions occurring in...

approach. Hasse–Weil L-function A Hasse–Weil L-function, sometimes called a global L-function, is an Euler product formed from local zeta-functions. The properties...

equipped with a function field F, which is a field extension of k. Each such function field gives rise to a Hasse–Weil zeta function ζF, and the Riemann...

curve over a finite field, and Hesselholt (2016) showed that the Hasse-Weil zeta-function of a smooth proper variety over Fp can be expressed using regularized...

elliptic curve E over a number field K to the behaviour of the Hasse–Weil L-function L(E, s) of E at s = 1. More specifically, it is conjectured that...

different fields. Weil (1949) used it to calculate the zeta function of a Fermat hypersurface over a finite field, which motivated the Weil conjectures. Gauss...