About: Weil's criterion

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In mathematics, Weil's criterion is a criterion of André Weil for the Generalized Riemann hypothesis to be true. It takes the form of an equivalent statement, to the effect that a certain generalized function is positive definite. Weil's idea was formulated first in a 1952 paper. It is based on the explicit formulae of prime number theory, as they apply to Dirichlet L-functions, and other more general . A single statement thus combines statements on the complex zeroes of all Dirichlet L-functions.

Attributes	Values
rdfs:label	Weil's criterion (en)
rdfs:comment	In mathematics, Weil's criterion is a criterion of André Weil for the Generalized Riemann hypothesis to be true. It takes the form of an equivalent statement, to the effect that a certain generalized function is positive definite. Weil's idea was formulated first in a 1952 paper. It is based on the explicit formulae of prime number theory, as they apply to Dirichlet L-functions, and other more general . A single statement thus combines statements on the complex zeroes of all Dirichlet L-functions. (en)
dct:subject	Zeta and L-functions
Wikipage page ID	5906027 (xsd:integer)
Wikipage revision ID	1040824443 (xsd:integer)
Link from a Wikipage to another Wikipage	Mathematics Generalized Riemann hypothesis Generalized function André Weil Positive-definite function Zeta and L-functions Explicit formula (L-function) Dirichlet L-function Artin L-function Artin conjecture (L-functions) Global function field dbr:Artin-Hecke_L-function dbr:Global_L-function
sameAs	Weil's criterion Weil's criterion Weil's criterion
has abstract	In mathematics, Weil's criterion is a criterion of André Weil for the Generalized Riemann hypothesis to be true. It takes the form of an equivalent statement, to the effect that a certain generalized function is positive definite. Weil's idea was formulated first in a 1952 paper. It is based on the explicit formulae of prime number theory, as they apply to Dirichlet L-functions, and other more general . A single statement thus combines statements on the complex zeroes of all Dirichlet L-functions. Weil returned to this idea in a 1972 paper, showing how the formulation extended to a larger class of L-functions; and to the global function field case. Here the inclusion of Artin L-functions, in particular, implicates Artin's conjecture; so that the criterion involves a Generalized Riemann Hypothesis plus Artin Conjecture. The case of function fields, of curves over finite fields, is one in which the analogue of the Riemann Hypothesis is known, by Weil's classical work begun in 1940; and Weil also proved the analogue of the Artin Conjecture. Therefore, in that setting, the criterion can be used to show the corresponding statement of positive-definiteness does hold. (en)
gold:hypernym	Criterion
prov:wasDerivedFrom	wikipedia-en:Weil's_criterion?oldid=1040824443&ns=0
page length (characters) of wiki page	1731 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weil's_criterion
is Link from a Wikipage to another Wikipage of	Riemann hypothesis André Weil Li's criterion List of things named after André Weil Weil criterion
is Wikipage redirect of	Weil criterion
is known for of	André Weil
is foaf:primaryTopic of	wikipedia-en:Weil's_criterion

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