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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
Weil's_criterion
Statement in number theory
Li's criterion is a particular statement about the positivity of a certain sequence that is equivalent to the Riemann hypothesis. The criterion is named
Li's_criterion
French mathematician (1906-1998)
André Weil (/veɪ/; French: [ɑ̃dʁe vɛj]; 6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic
André_Weil
Conjecture on zeros of the zeta function
<1} . Weil's criterion is the statement that the positivity of a certain function is equivalent to the Riemann hypothesis. Related is Li's criterion, a statement
Riemann_hypothesis
Map Weil–Châtelet group Weil cohomology Weil conjecture (disambiguation) Weil conjectures Weil conjecture on Tamagawa numbers Weil's criterion Weil–Deligne
List of things named after André Weil
List_of_things_named_after_André_Weil
French philosopher (1909–1943)
2011 – via HighBeam Research. Erica DaCosta (June 2004). "The Four Simone Weils" (PDF). The Women's Review of Books. 21 (9): 7–8. doi:10.2307/4024308. JSTOR 4024308
Simone_Weil
Mathematical function associated to algebraic varieties
This manifests itself in the étale theory in the Néron–Ogg–Shafarevich criterion for good reduction; namely that there is good reduction, in a definite
Hasse–Weil_zeta_function
German-born French philosopher
political identity. Weil was born June 8, 1904, in the town of Parchim in the German Empire, to Louis and Ida (née Löwenstein) Weil. The Weils were a well-to-do
Éric_Weil
Book by George Steiner
Boulanger and Simone Weil. The book is based on Steiner's Norton lectures. Dean, Paul (January 2004). "The Steiner school (Book)". New Criterion. 22 (5): 73–75
Lessons_of_the_Masters
United States obscenity law expression
serious literary, artistic, political, or scientific value. The third criterion pertains to judgment made by "reasonable persons" of the United States
I_know_it_when_I_see_it
with U.S. distribution rights currently licensed to Janus Films and The Criterion Collection Owned by Film Associates International, with North American
List_of_Miramax_films
1995 publication in mathematics
the same cardinality. This is sometimes referred to as the "numerical criterion". Given this result, Fermat's Last Theorem is reduced to the statement
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Topics referred to by the same term
theorem, named for Igor Shafarevich, may refer to: Néron–Ogg–Shafarevich criterion Golod–Shafarevich theorem about class field towers Grothendieck–Ogg–Shafarevich
Shafarevich_theorem
Irish actress
reimagined as Close to You when it moved to the Criterion Theatre. She took over the role of Cynthia Weil in Beautiful: The Carole King Musical for its
Stephanie_McKeon
Representation theory of the symplectic group
symplectic group, first investigated by Irving Segal, David Shale, and André Weil. A natural extension of the representation leads to a semigroup of contraction
Oscillator_representation
1987 film by Norman Jewison
in 1998. It was released on Blu-ray by MGM on February 15, 2011. The Criterion Collection released a remastered Blu-ray on November 17, 2020. Soundtrack
Moonstruck
Claude Chevalley and André Weil pointed out to Oscar Zariski (1947) that, over non-perfect fields, the Jacobian criterion for a simple point of an algebraic
Geometrically_regular_ring
Journal für die reine und angewandte Mathematik (in French), 3: 390–393 Weil, André; Rosenlicht, Maxwell (1979), "§ VIII", Number Theory for beginners
Proofs of Fermat's little theorem
Proofs_of_Fermat's_little_theorem
1974 film by John Cassavetes
Touchstone Home Video released the film on VHS. On September 21, 2004, The Criterion Collection released the film—together with Shadows (1959), Faces (1968)
A_Woman_Under_the_Influence
1955 book by Raymond Aron
ISBN 978-1412813907. Kimball, Roger. "The Opium of the Intellectuals". New Criterion. Archived from the original on 8 August 2014. Retrieved 4 August 2014
The Opium of the Intellectuals
The_Opium_of_the_Intellectuals
German, Jewish, and American historian and philosopher (1906–1975)
transcription) Teichman, Jenny (April 1994). "Understanding Arendt". The New Criterion (Review). — (2005). Ludz, Ursula (ed.). Ich will verstehen: Selbstauskünfte
Hannah_Arendt
Symmetric bilinear form in mathematics
theories of Lie groups and Lie algebras. Cartan's criteria (criterion of solvability and criterion of semisimplicity) show that Killing form has a close relationship
Killing_form
primes of bad reduction of the curve: this is the Néron–Ogg–Shafarevich criterion. Ogg's formula expresses the conductor in terms of the discriminant and
Conductor of an elliptic curve
Conductor_of_an_elliptic_curve
German mathematician (1823–1852)
AMS Chelsea Publishing, ISBN 978-0-8284-1280-3, MR 0427029 Weil's review Eisenstein's criterion Eisenstein ideal Eisenstein integer Eisenstein prime Eisenstein
Gotthold_Eisenstein
American film director and screenwriter (born 1959)
NoFilmSchool. Retrieved September 5, 2023. "The Criterion Channel's September 2023 Lineup". The Criterion Channel. August 21, 2023. Retrieved September
Hal_Hartley
French philosopher and sociologist (1798–1857)
irrespective of the wishes of anyone...This Comte accomplished by taking as the criterion of the position of each the degree of what he called "positivity", which
Auguste_Comte
Mathematical law, a generalization of quadratic reciprocity
{p}}} for m {\displaystyle m} and vice versa by the comparatively simple criterion whether ( − 1 ) p − 1 2 q − 1 2 {\displaystyle (-1)^{{\frac {p-1}{2}}{\frac
Reciprocity_law
Psychological concept
Individuals' set point may merely be a genetic tendency not a heritable criterion for happiness. In a study on moderate to excessive drug intake in rats
Hedonic_treadmill
than 25,000. As of May 15, 2022, 74 cities and municipalities meet this criterion and are included on this list. This list refers only to the population
List of cities in Baden-Württemberg by population
List_of_cities_in_Baden-Württemberg_by_population
23 mathematical problems stated in 1900
them in the published list. The "24th problem" (in proof theory, on a criterion for simplicity and general methods) was rediscovered in Hilbert's original
Hilbert's_problems
Irish-born British writer and philosopher (1919–1999)
attained by them. In The Sovereignty of Good, Murdoch argues that such a criterion of reality follows from the adoption of an "uncriticized conception of
Iris_Murdoch
Successful media that was initially unsuccessful
Ganeri & Bergan 2006, p. 458. Crawford, Travis (16 December 2010). "Criterion: American Lost and Found: The BBS Story". Filmmaker Magazine. Retrieved
Sleeper_hit
Awards that are unrestricted by genre
to musical acts and works which are not restricted by genre or another criterion. The Big Four are part of the General Field, which encompasses six categories
Big_Four_(Grammy_Awards)
1976 film by John Cassavetes
he did for his friend Cassavetes in the 1970s. In an interview for the Criterion Collection in the mid-2000s, Gazzara stated that he believed that Vittelli
The Killing of a Chinese Bookie
The_Killing_of_a_Chinese_Bookie
American actor (born 1971)
Valley. "Noah Wyle's Closet Picks". youtube.com/@criterioncollection. criterion.com. Retrieved June 23, 2026. "Who Do You Think You Are? – Season 8, Episode
Noah_Wyle
French filmmaker and actor (1907–1982)
expensive work of Tati's career.[citation needed] In an essay for the Criterion Collection, Kent Jones wrote: After the success of Mon Oncle in 1958,
Jacques_Tati
American actor (born 1938)
dated actresses Diane Baker and Elizabeth Taylor. He was married to Ruth Weil from November 6, 1977, to their divorce in 1995. They have two children,
Frank_Langella
Chinese Confucian philosopher (c. 310 – after 238 BCE)
measurements promoted by the Legalists, as the wellspring of objective criterion. His ideal gentleman (junzi) king and government, aided by a class of
Xunzi_(philosopher)
American musician and actor (1942–2019)
Guitar World, July 26, 2013. "America Lost and Found: The BBS Story". The Criterion Channel. Archived from the original on February 22, 2019. Retrieved February
Peter_Tork
Matrix used in complex analysis
Wiley-Interscience, ISBN 978-0-471-57127-8 Takhtajan, Leon A.; Teo, Lee-Peng (2006), "Weil–Petersson metric on the universal Teichmüller space", Mem. Amer. Math. Soc
Grunsky_matrix
1952 Italian film
(DVD). The Criterion Collection. Interview with Isabella Rossellini in: 3 Films by Roberto Rossellini Starring Ingrid Bergman (DVD). The Criterion Collection
Europe_'51
American philosopher (1901–1985)
National Interest National Review The New American The New Atlantis The New Criterion Policy Review (defunct) Southern Partisan Spectator USA Tablet Taki's
Eric_Voegelin
ramification in the field of division points by the Néron–Ogg–Shafarevich criterion. The theory is subtle, in the sense that the freedom to change variables
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
Legal order saying not to perform CPR if heart stops
respiration, and irreversible absence of whole brain function. Only one criterion needs to be met for the determination of death before organ donation and
Do_not_resuscitate
Projective variety that is also an algebraic group
condition imposes extra constraints on a complex torus. The following criterion by Riemann decides whether or not a given complex torus is an abelian
Abelian_variety
1943 novel by Ayn Rand
Michael J. (December 2007). "The Rise of the 'Starchitect'". The New Criterion. Vol. 26, no. 4. Retrieved September 20, 2017. Mayhew, Robert, ed. (2006)
The_Fountainhead
Algebraic structure used in analysis
all of g l ( n , F ) {\displaystyle {\mathfrak {gl}}(n,F)} . Cartan's criterion (by Élie Cartan) gives conditions for a finite-dimensional Lie algebra
Lie_algebra
English philosopher and jurist (1748–1832)
benchmark, or what he called the "insuperable line". If reason alone were the criterion by which we judge who ought to have rights, human infants and adults with
Jeremy_Bentham
German philosopher and sociologist (1895–1973)
conforming, and easily furnishes ideology. In instrumental reason, the sole criterion of reason is its operational value or purposefulness, and with this, the
Max_Horkheimer
Scottish essayist, historian and philosopher (1795–1881)
November 2023. Swaim, Barton (February 2010). "Carlyle the wise". The New Criterion. Retrieved 14 November 2023. Sussman, Herbert L. (1979). Fact into Figure:
Thomas_Carlyle
66–68. Teichman, Jenny (April 1994). "Understanding Arendt". The New Criterion (Review). — (2005). Ludz, Ursula (ed.). Ich will verstehen: Selbstauskünfte
List of works by Hannah Arendt
List_of_works_by_Hannah_Arendt
Beatified German Augustinian canoness and mystic (1774–1824)
what is embroidery or additions, we could not take these writings as a criterion [in the decision on beatification]. Therefore, they were simply discarded
Anne_Catherine_Emmerich
Repeating 3 to 6-syllable section of a poetic metre
suggested another criterion, namely that a metron often ends at a place where there is often a break in the syntax. Using this criterion Farzaad analysed
Metron_(poetry)
Number divisible only by 1 and itself
by three of the points has large area. Another example is Eisenstein's criterion, a test for whether a polynomial is irreducible based on divisibility
Prime_number
Chief Justice of the United States from 1986 to 2005
suburban Shorewood High School, just outside Milwaukee, weather was a key criterion in selecting a college. "Illinois General Assembly - Full Text of HR0622"
William_Rehnquist
American philosopher and psychologist (1842–1910)
after they are experienced, but are necessarily confined by the first criterion of ineffability, and are thus inexpressible in words. Transiency – the
William_James
Algebraic variety of dimension two
using the Nakai criterion and the Riemann-Roch theorem for surfaces. The Hodge index theorem is used in Deligne's proof of the Weil conjecture. Basic
Algebraic_surface
English actor (1913–1994)
success in a 1945 production of Sheridan's The Rivals at Westminster's Criterion Theatre, which earned him enough money to pay off some growing debts.
Peter_Cushing
Law in algebraic number theory
{\displaystyle a=b^{l}.} Quartic reciprocity Octic reciprocity Wieferich's criterion Mirimanoff's congruence Lemmermeyer, p. 392. Ireland & Rosen, ch. 14.2
Eisenstein_reciprocity
Scottish philosopher, historian, economist and essayist (1711–1776)
liveliness and vivacity—what Henry E. Allison (2008) calls the "FLV criterion". Ideas are therefore "faint" copies of impressions. For example, experiencing
David_Hume
20th-century rise in intelligence test scores
ISBN 978-0-470-89127-8. Both definitions also specify that the intellectual functioning criterion for a diagnosis of intellectual disability is approximately 2 SDs or more
Flynn_effect
Burnside's p α q β {\displaystyle p^{\alpha }q^{\beta }} solvability criterion using such methods, its power was soon appreciated. Later Richard Brauer
History of representation theory
History_of_representation_theory
Italian philosopher (1668–1744)
observation: "The criterion and rule of the true is to have made it. Accordingly, our clear and distinct idea of the mind cannot be a criterion of the mind
Giambattista_Vico
German composer (born 1966 in Hameln )
Reviews Peter Richardson's How To Die in Oregon [SXSW 2011 Review]". CriterionCast. 26 March 2011. Retrieved 29 November 2013. ""Unforgivable" von André
Max_Richter
German mathematician (1862–1943)
polynomial over it has a root in it. Under this condition, Hilbert gave a criterion for when a collection of polynomials ( p λ ) λ ∈ Λ {\displaystyle (p_{\lambda
David_Hilbert
Slovenian philosopher (born 1949)
madness: the list contains only 'guilty pleasures'". In his tour of The Criterion Collection closet, he chose Trouble in Paradise, Sweet Smell of Success
Slavoj_Žižek
ranked highly enough to be considered a realistic medal contender. Per a criterion change in late 2023, male Dutch golfers would have to finish in the top
Concerns and controversies at the 2024 Summer Olympics
Concerns_and_controversies_at_the_2024_Summer_Olympics
American philosopher, psychologist, and activist (1859–1952)
effectively in a great variety of occupations and situations, is a sign and a criterion of the degree of civilization that a society has reached. It is the business
John_Dewey
1970 book by Iris Murdoch
different one. She argues that philosophy's attachment to observability as a criterion of reality stems from its adoption of an "uncriticized conception of science"
The_Sovereignty_of_Good
Russian writer (1828–1910)
Brace. Morson, Gary Saul (2019). "The greatest of all novels". The New Criterion. Archived from the original on 28 December 2023. Retrieved 28 December
Leo_Tolstoy
English philosopher (1944–2020)
phenomena uproot old identities and forms of belonging." Writing in The New Criterion, Daniel J. Mahoney finds that Scruton was "defender of the soul and civilization"
Roger_Scruton
Dutch philosopher and theologian (c. 1466–1536)
ISBN 0-7509-1406-8. Kuhner, John Byron (2017). "The Vatican's Latinist". The New Criterion. 25 (7). Archived from the original on 6 June 2017. Retrieved 3 March
Erasmus
Finite sum formed using the exponential function
distribution of the values ƒ(n) modulo 1, according to Weyl's equidistribution criterion. A basic advance was Weyl's inequality for such sums, for polynomial f
Exponential_sum
Scientific study of human society and relationships
thought of as somehow objectively 'correct' or 'true' by some metaphysical criterion. This is the difference between the empirical sciences of action, such
Sociology
sites that the media have been citing, have been criticized for using a criterion much more inclusive than that used by the government—they count four victims
Gun violence in the United States
Gun_violence_in_the_United_States
Genevan philosopher, writer, and composer (1712–1778)
if renewed on Rousseau's principles. France could not meet Rousseau's criterion of an ideal state because it was too big. Much subsequent controversy
Jean-Jacques_Rousseau
Standard, doctrine or system of conduct
Haidt has noted that experimental observation indicating an in-group criterion provides one moral foundation substantially used by conservatives, but
Morality
Classical Athenian statesman and orator (384–322 BC)
to Professor of Greek Arthur Wallace Pickarde, success may be a poor criterion for judging the actions of people like Demosthenes, who were motivated
Demosthenes
Jewish Ghetto Policeman Lewis, Tess. "A brighter, clearer light". The New Criterion. October 2002. " Completely assimilated and an atheist, Reich-Ranicki
List of Jewish atheists and agnostics
List_of_Jewish_atheists_and_agnostics
Natural dispositions and characteristics that humans possess
that specifies possessing human nature as a necessary and sufficient criterion for belonging to the human species. Invariances that assume the understanding
Human_nature
Attitude of a person towards work
internal consistency reliability, temporal stability, convergent and criterion-related validities, but also for cross-population invariance by nationality
Job_satisfaction
Chinese ethical and philosophical system
dualistic relationship between sacred and profane and to use this as a criterion of religion is to beg the question of whether Confucianism can count as
Confucianism
Multi-year debt crisis in multiple EU countries, 2009–2010
Fund Facility, and Request for Waiver of Nonobservance of Performance Criterion and Rephasing of Access; Staff Report; Press Release; and Statement by
Euro_area_crisis
Framework in macroeconomics
of an equilibrium is strongly linked to the interest rate and the Cass Criterion gives necessary and sufficient conditions for when an OLG competitive
Overlapping_generations_model
Chinese-American mathematician (born 1949)
[Y82b] During the 1980s, Yau and others came to understand that this criterion could not be sufficient. Inspired by the Donaldson−Uhlenbeck−Yau theorem
Shing-Tung_Yau
Palestinian-American academic (1935–2003)
Lewis was saying that "knowledge about Europe [was] the only acceptable criterion for true knowledge." The appearance of academic impartiality was part
Edward_Said
Theorem in algebraic geometry
Chevalley's structure theorem is used in the proof of the Néron–Ogg–Shafarevich criterion. Barsotti, Iacopo (1955a), "Structure theorems for group-varieties", Annali
Chevalley's_structure_theorem
In mathematics, a type of algebra
{\displaystyle [{\mathfrak {g}},{\mathfrak {g}}]} . This is Cartan's criterion for solvability. Lie's Theorem states that if V {\displaystyle V} is a
Solvable_Lie_algebra
Chemical compound
and the glow wire flammability test (GWFI) at 960 °C. Another important criterion in E&E applications is the Comparative Tracking Index (CTI), which determines
Aluminium_diethyl_phosphinate
modulo n Multiplicative order Discrete logarithm Quadratic residue Euler's criterion Legendre symbol Gauss's lemma (number theory) Congruence of squares Luhn
List_of_number_theory_topics
Anti-establishment cultural phenomenon
original on December 19, 2013. Retrieved March 19, 2012. "Monterey Pop". The Criterion Collection. Kilgannon, Corey (March 17, 2009). "3 Days of Peace and Music
Counterculture_of_the_1960s
Chinese mathematician (born 1958)
Criterion". International Mathematics Research Notices. 2024 (17): 12150–12160. doi:10.1093/imrn/rnae160. ISSN 1073-7928. Todorov, Andrey N. The Weil-Petersson
Tian_Gang
American philosopher (1932–2025)
statement is evaluable, in fact, falsifiable, by an understood ("background") criterion for mountain height, such as "the summit is so many meters above sea level"
John_Searle
Engineering discipline
being analyzed either breaks or is deformed plastically, depending on the criterion for failure. Fatigue failure occurs when an object fails after a number
Mechanical_engineering
American poet (1917–1977)
2013. "The achievement of Robert Lowell by Richard Tillinghast". The New Criterion. Retrieved May 30, 2013. AO Scott's Collected Poems review on Slate "A
Robert_Lowell
transformation Lie's third theorem Maurer–Cartan form Cartan's theorem Cartan's criterion Local Lie group Formal group law Hilbert's fifth problem Hilbert–Smith
List_of_Lie_groups_topics
American business-focused daily newspaper
won the 1997 Pulitzer Prize for National Reporting about AIDS. Jonathan Weil, a reporter at the Dallas bureau of The Wall Street Journal, is credited
The_Wall_Street_Journal
Long-distance hiking trail in Germany
Deutschland". (Quality Trail of Hikable Germany). In order to meet a criterion for this certification, that no more than 20% of the trail could be paved
Westweg
Algebraic variety in a projective space
definition, a variety is complete, if it is proper over k. The valuative criterion of properness expresses the intuition that in a proper variety, there
Projective_variety
1987 book by Thomas Sowell
National Interest National Review The New American The New Atlantis The New Criterion Policy Review (defunct) Southern Partisan Spectator USA Tablet Taki's
A_Conflict_of_Visions
travel, tourism, insurance
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