About: Siegel zero

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In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero (also known as exceptional zero), named after Edmund Landau and Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these are possible zeros very near (in a quantifiable sense) to .

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rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Siegel-Nullstelle (de) Cero de Siegel (es) Zéro de Siegel (fr) Zero di Siegel (it) Siegel zero (en) Zero de Siegel (pt) 西格尔零点 (zh)
rdfs:comment	In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero (also known as exceptional zero), named after Edmund Landau and Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these are possible zeros very near (in a quantifiable sense) to . (en) Em matemática, mais especificamente na área de teoria analítica dos números, um zero de Landau–Siegel ou simplesmente zero de Siegel (também conhecido como zero excepcional), nomeado em homenagem a Edmund Landau e Carl Ludwig Siegel, é um tipo de contraexemplo potencial para a Hipótese de Riemann generalizada, sobre zeros de funções L de Dirichlet associadas a corpos de números quadráticos. Grosso modo, estes são possíveis zeros muito próximos (num sentido quantificável) de s = 1. (pt) Die Siegel-Nullstelle (auch Landau-Siegel-Nullstelle) bezeichnet in der analytischen Zahlentheorie ein potentielles Gegenbeispiel, um die verallgemeinerte Riemannsche Vermutung zu widerlegen. Diese Vermutung weitet die klassische Riemannsche Vermutung auf Dirichletsche L-Funktionen aus. Es handelt sich um eine hypothetische Nullstelle einer L-Funktion in der Nähe des Wertes . Für eine L-Funktion kann es höchstens eine Siegel-Nullstelle geben. Die Landau-Siegel-Nullstelle ist nach den deutschen Mathematikern Carl Ludwig Siegel und Edmund Landau benannt. (de) En matemáticas, más específico en el campo de Teoría analítica de números, un cero de Siegel, en honor a Carl Ludwig Siegel, es un tipo de contraejemplo potencial de la hipótesis de Riemann generalizada, sobre los ceros de las funciones L de Dirichlet. Existen valores hipotéticos s de una variable compleja, muy cercanas (en un sentido cuantificable) a 1, tal que L(s,χ) = 0 La posibilidad de un cero de Siegel en términos analíticos se refiere a un estimativo muy poco efectivo L(1,χ) > C(ε)q−ε donde C está en función de ε para el cual la prueba no provee de forma explícita una cota inferior. (es) En mathématiques, plus précisément en théorie analytique des nombres, un zéro de Siegel (ainsi nommé d'après Carl Ludwig Siegel) est un contre-exemple potentiel à l'hypothèse de Riemann généralisée sur les zéros des fonctions L de Dirichlet. L'existence éventuelle d'un zéro de Siegel mène à l'estimation non effective L(1,χ) > C(ε)q–ε pour tout ε > 0, où q désigne le module du caractère χ et C(ε) > 0 est un réel pouvant dépendre de ε.Lorsque ε < 1/2, la démonstration de cette inégalité ne fournit pas de valeur explicite de C(ε) (voir également résultats effectifs en théorie des nombres). (fr) Nella teoria dei numeri analitica, uno zero di Siegel, dal nome del matematico tedesco Carl Ludwig Siegel, è un tipo di potenziale controesempio all'ipotesi di Riemann generalizzata, sugli zeri della funzione L di Dirichlet. Esistono ipotetici valori s di una variabile complessa, molto vicini (in senso quantificabile) ad 1, così che per un carattere di Dirichlet , detto di modulo q. La possibilità di uno zero di Siegel in termini analitici porta ad una stima incerta di dove C è una funzione di ε per la quale la dimostrazione prevede l'inesistenza di un esplicito limite inferiore. (it)
dcterms:subject	Zeta and L-functions
Wikipage page ID	1967197 (xsd:integer)
Wikipage revision ID	1122220614 (xsd:integer)
Link from a Wikipage to another Wikipage	Carl Ludwig Siegel Prime number theorem Quadratic number field Roger Heath-Brown Root of unity Homomorphism Peter J. Weinberger Upper and lower bounds Dedekind zeta function Deuring–Heilbronn phenomenon Zeros and poles Analytic continuation Mathematics Generalized Riemann hypothesis Class number formula Entire function Andrew Granville Arithmetic function Completely multiplicative function Complex conjugate Complex multiplication Fundamental discriminant Fundamental unit (number theory) Ideal class group Kronecker symbol Kronecker–Weber theorem Primes in arithmetic progression Twin prime Linnik's theorem Abc conjecture Analytic number theory Zeta and L-functions Edmund Landau Erich Hecke Euler product Brauer–Siegel theorem Dirichlet L-function Dirichlet series Discriminant of an algebraic number field Hilbert class field Pierre Colmez Quadratic reciprocity Residue (complex analysis) Harold Stark Height function J-invariant Counterexample Terence Tao Abelian extension Binary quadratic form Biquadratic field Effective results in number theory Artin L-function Artin reciprocity law Class number problem Idoneal number Generalized Riemann Hypothesis Sieve theory Siegel–Walfisz theorem Dorian Goldfeld Complex variable dbr:Linear_sieve dbr:Tikao_Tatsuzawa
Link from a Wikipage to an external page	https://link.springer.com/book/10.1007/978-1-4757-5927-3 https://www.cambridge.org/core/books/multiplicative-number-theory-i/4E45519B26115AEEA4839C6C38206ACD https://www.springer.com/de/book/9783540106036
sameAs	Siegel zero Siegel zero Siegel zero Siegel zero Siegel zero Siegel zero Siegel zero Siegel zero Siegel zero

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