About: Explicit formulae for L-functions

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In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function. Such explicit formulae have been applied also to questions on bounding the discriminant of an algebraic number field, and the conductor of a number field.

Attributes	Values
rdfs:label	Fórmula explícita (es) Explicit formulae for L-functions (en) 明示公式 (ja) Fórmula explícita (pt)
rdfs:comment	In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function. Such explicit formulae have been applied also to questions on bounding the discriminant of an algebraic number field, and the conductor of a number field. (en) En matemática, la fórmula explícita para funciones L son un conjunto de ecuaciones que relacionan sumas sobre «ceros complejos» o «no triviales» de una función L con sumas sobre potencias de primos, introducida por primera vez por Bernhard Riemann para la función zeta de Riemann. Tales fórmulas explícitas también han sido aplicadas a otras ramas de la matemática como pueden ser cuestiones sobre los límites de discriminantes del campo de los números algebraicos.Es cuando la variable dependiente o función está despejada (es) 数学では、L-函数の明示公式(explicit formulae for L-function)は、L-函数の複素数の零点を渡る総和と素数冪を渡る総和との関係のことを言い、リーマンゼータ函数についてにより導入された。明示公式は、(discriminant of an algebraic number field)や導手の境界に関する問題への応用も持っている。 (ja) Em matemática, a fórmula explícita para funções L são relações entre somas sobre os números complexos zero de uma função L e soma entre potências de primos, introduzidos por Riemann em 1859 para a função zeta de Riemann. Tais fórmulas explícitas tem sido aplicadas também a questões sobre delimitações ao , e o . (pt)
dcterms:subject	Zeta and L-functions
Wikipage page ID	2205110 (xsd:integer)
Wikipage revision ID	1118077980 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Prime-counting function Prime number theorem On the Number of Primes Less Than a Given Magnitude Residue theorem Riemann zeta function Von Mangoldt function Dedekind zeta function L-function The Mathematical Intelligencer Analytic continuation Mathematics Generalized Riemann hypothesis Eigenvalue Generalized function Branch point Möbius function André Weil Linear operator Local zeta-function Cauchy principal value Topological group Logarithmic integral function Alain Connes Zeta and L-functions Duke Math. J. Dirichlet L-function Dirichlet character Discriminant of an algebraic number field Hilbert–Pólya conjecture Hans Carl Friedrich von Mangoldt Absolute convergence Digamma function Dirac delta function Natural logarithm Selberg trace formula Springer-Verlag Hecke L-series Journal für die reine und angewandte Mathematik Chebyshev's function Conductor of a number field Robert Charles Vaughan (mathematician)
Link from a Wikipage to an external page	http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/ https://encyclopediaofmath.org/wiki/M%C3%B6bius_function%23:~:text=The%20M%C3%B6bius%20function%20is%20an,M%C3%B6bius%20in%201832
sameAs	Explicit formulae for L-functions Explicit formulae for L-functions Explicit formulae for L-functions Explicit formulae for L-functions Explicit formulae for L-functions
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Clarify dbt:Efn dbt:Frac dbt:Harvtxt dbt:Math dbt:Mvar dbt:Notelist dbt:Pad dbt:Reflist dbt:Unreferenced_section dbt:Harvnb
date	September 2020 (en)
reason	The relation of this to the preceding material needs to be explained. (en) A formula by this name is not mentioned in the article. (en)
has abstract	In mathematics, the explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by for the Riemann zeta function. Such explicit formulae have been applied also to questions on bounding the discriminant of an algebraic number field, and the conductor of a number field. (en) En matemática, la fórmula explícita para funciones L son un conjunto de ecuaciones que relacionan sumas sobre «ceros complejos» o «no triviales» de una función L con sumas sobre potencias de primos, introducida por primera vez por Bernhard Riemann para la función zeta de Riemann. Tales fórmulas explícitas también han sido aplicadas a otras ramas de la matemática como pueden ser cuestiones sobre los límites de discriminantes del campo de los números algebraicos.Es cuando la variable dependiente o función está despejada (es) 数学では、L-函数の明示公式(explicit formulae for L-function)は、L-函数の複素数の零点を渡る総和と素数冪を渡る総和との関係のことを言い、リーマンゼータ函数についてにより導入された。明示公式は、(discriminant of an algebraic number field)や導手の境界に関する問題への応用も持っている。 (ja) Em matemática, a fórmula explícita para funções L são relações entre somas sobre os números complexos zero de uma função L e soma entre potências de primos, introduzidos por Riemann em 1859 para a função zeta de Riemann. Tais fórmulas explícitas tem sido aplicadas também a questões sobre delimitações ao , e o . (pt)
prov:wasDerivedFrom	wikipedia-en:Explicit_formulae_for_L-functions?oldid=1118077980&ns=0
page length (characters) of wiki page	15410 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Explicit_formulae_for_L-functions
is Link from a Wikipage to another Wikipage of	Riemann's explicit formula Explicit formula (L-function) Explicit formulae (L-function) Poisson summation formula Explicit formula of an L-function Weil's explicit formula
is Wikipage redirect of	Riemann's explicit formula Explicit formula (L-function) Explicit formulae (L-function) Explicit formula of an L-function Weil's explicit formula
is foaf:primaryTopic of	wikipedia-en:Explicit_formulae_for_L-functions

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