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...

In mathematics, 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...

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...

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...

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...

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...

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...

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...

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...

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...

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

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

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

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

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...

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...

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...

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...

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...

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...

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

\zeta _{C}(s)=\zeta _{k}(s)\zeta _{k}(s-1)/L_{C}(s)} is the zeta function of C {\displaystyle C} over k {\displaystyle k} . If the Hasse–Weil conjecture is...

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...

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...

needs to express the Hasse–Weil L-functions of the Fermat curves, for example. The exact conductors of these characters, a question Weil had left open, were...

In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite...