Weil's Criterion
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Weil's Criterion

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High Quality Content by WIKIPEDIA articles! 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 global L-functions. A single statement thus combines statements on the complex zeroes of all Dirichlet L-functions. Weil returned to this idea in a 19...