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The Dwork conjecture (1973) states that his unit root zeta function is p-adic meromorphic everywhere. This conjecture was proved by Wan (2000). Dwork, Bernard
Dwork_conjecture
American mathematician
first part of the Weil conjectures: the rationality of the zeta function of a variety over a finite field. The general theme of Dwork's research was p-adic
Bernard_Dwork
Proposition in mathematics that is unproven
In mathematics, a conjecture is a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis or
Conjecture
On generating functions from counting points on algebraic varieties over finite fields
suggestions from Serre. The rationality part of the conjectures was proved first by Bernard Dwork (1960), using p-adic methods. Grothendieck (1965) and
Weil_conjectures
Unsolved problem in computational complexity theory
Unique Games Conjecture true? More unsolved problems in computer science In computational complexity theory, the unique games conjecture (often referred
Unique_games_conjecture
Topics referred to by the same term
The term Weil conjecture may refer to: The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne
Weil_conjecture
2001 Yves André, Sur la conjecture des p-courbures de Grothendieck–Katz et un problème de Dwork, in Geometric Aspects of Dwork Theory (2004), editors Alan
Grothendieck–Katz p-curvature conjecture
Grothendieck–Katz_p-curvature_conjecture
Connection on a vector bundle
transcendental number theory, for meromorphic function solutions. The Bombieri–Dwork conjecture, also attributed to Yves André, which is given in more than one version
Gauss–Manin_connection
involving the geometric genus would have significant consequences. Dwork's method Bernard Dwork used distinctive methods of p-adic analysis, p-adic algebraic
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
American mathematician (1925–2019)
D. advisor. His students include George Bergman, Ted Chinburg, Bernard Dwork, Benedict Gross, Robert Kottwitz, Jonathan Lubin, Stephen Lichtenbaum, James
John_Tate_(mathematician)
Theorem about complexity measures of Boolean functions
1\}^{n}\to \{0,1\}} is at least the square root of its degree, thus settling a conjecture posed by Nisan and Szegedy in 1992. The proof is notably succinct, given
Sensitivity_theorem
Mathematical conjecture
as the variety X {\displaystyle X} and a construction from the quintic Dwork family X ψ {\displaystyle X_{\psi }} giving X ˇ = X ~ ψ {\displaystyle {\check
Mirror_symmetry_conjecture
Chinese mathematician (born 1964)
particularly zeta functions over finite fields. He is known for his proof of Dwork's conjecture that the p-adic unit root zeta function attached to a family of varieties
Daqing_Wan
French mathematician (1906-1998)
intensively). The so-called Weil conjectures were hugely influential from around 1950; these statements were later proved by Bernard Dwork, Alexander Grothendieck
André_Weil
Branch of algebraic geometry
later scheme theory, in the 1950s and 1960s. Bernard Dwork proved one of the four Weil conjectures (rationality of the local zeta function) in 1960. Grothendieck
Arithmetic_geometry
3d hypersurface of degree 5
class of examples of quintic three-folds, studied in many contexts, is the Dwork family. One popular study of such a family is from Candelas, De La Ossa
Quintic_threefold
Hypothesis in computational complexity theory
Computing (STOC). pp. 333–342. doi:10.1145/1536414.1536461. Ajtai, Miklós; Dwork, Cynthia (1997). "A Public-Key Cryptosystem with Worst-Case/Average-Case
Computational hardness assumption
Computational_hardness_assumption
Prize awarded by the American Mathematical Society
Mathematical Society. 65 (4): 183–226. doi:10.1090/S0002-9904-1959-10317-7. Dwork, Bernard (1960). "On the rationality of the zeta function of an algebraic
Cole_Prize
Weil cohomology theory for schemes X over a base field k
cohomology is partly inspired by the p-adic proof in Dwork (1960) of part of the Weil conjectures and is closely related to the algebraic version of de
Crystalline_cohomology
American mathematician (born 1943)
degree and in 1966 he received his doctorate under supervision of Bernard Dwork with thesis On the Differential Equations Satisfied by Period Matrices.
Nick_Katz
Sheaf cohomology on the étale site
to prove some of the Weil conjectures (Bernard Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods)
Étale_cohomology
Mathematical theory
introduction to the theory of p-adic representations", Geometric aspects of Dwork theory, vol. I, Berlin: Walter de Gruyter GmbH & Co. KG, arXiv:math/0210184
P-adic_Hodge_theory
23 mathematical problems stated in 1900
fields of algebraic geometry and number theory. The first conjecture was proven by Bernard Dwork; a different proof of the first two, via ℓ-adic cohomology
Hilbert's_problems
Austrian mathematician (1898–1962)
second conjecture, assuming certain cases of the generalized Riemann hypothesis. Artin advised over thirty doctoral students, including Bernard Dwork, Serge
Emil_Artin
Dutch-Australian number theorist
solution of Pisot's conjecture on the rationality of Hadamard quotients of rational functions, his 1992 work with Bernard Dwork on the Eisenstein constant
Alfred_van_der_Poorten
first proof uses the definition of E p ( x ) {\displaystyle E_{p}(x)} and Dwork's lemma, which says that a power series f ( x ) {\displaystyle f(x)} with
Artin–Hasse_exponential
Optimization problem in computer science
optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the construction of secure
Lattice_problem
out of proofs). See also list of axioms, list of theorems and list of conjectures. Abhyankar's lemma Aubin–Lions lemma Bergman's diamond lemma Fitting
List_of_lemmas
Elementary function in mathematics
constants in the case that ρ {\displaystyle \rho } is one-dimensional. Bernard Dwork proved the existence of the local constant ε ( ρ v , s , ψ v ) {\displaystyle
Langlands–Deligne local constant
Langlands–Deligne_local_constant
Branch of algebraic number theory concerned with abelian extensions
developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the
Class_field_theory
American mathematician
the Waring-Goldbach Problem (1968 or 1969) was advised by Bernard Morris Dwork. While working on his PhD at Princeton, he had a job as a Scientific Programmer
Stefan_Burr
Graduate-level textbooks in mathematics
1993-08-23 218 978-0691000961 133 An Introduction to "G"-Functions. Bernard Dwork, Giovanni Gerotto, Francis J. Sullivan 1994-05-02 352 978-0691036816 134
Annals_of_Mathematics_Studies
Dawidowicz 1975, pp. 384–385. Dwork & van Pelt 2002, p. 119. Cragg 2024, pp. 63–68. Dwork & van Pelt 2002, pp. 119–120. Dwork & van Pelt 2002, p. 121. Bauer
Responsibility for the Holocaust
Responsibility_for_the_Holocaust
books and 100 papers on project management and software development Cynthia Dwork (Ph.D. 1983 computer science) – distinguished computer scientist at Microsoft
List of Cornell University alumni (natural sciences)
List_of_Cornell_University_alumni_(natural_sciences)
History of maths
Grothendieck Fibred categories. 1959 Bernard Dwork Proves the rationality part of the Weil conjectures (the first conjecture). 1959 Jean-Pierre Serre Algebraic
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
2011 American film
film's release. The panel for the post-film discussion featured Debórah Dwork, PhD, director, Center for the Study of the Holocaust, Genocide, and Crimes
The_Rescuers_(2011_film)
Serre, Rationalité des fonctions zêta des variétés algébriques, d'après Dwork (local zeta-functions) Pierre Cartier, Structures simpliciales (simplicial
Séminaire Nicolas Bourbaki (1950–1959)
Séminaire_Nicolas_Bourbaki_(1950–1959)
DWORK CONJECTURE
DWORK CONJECTURE
Girl/Female
Arabic
Work
Girl/Female
Tamil
Hard work
Boy/Male
Hindu, Indian, Marathi
Hard Work
Surname or Lastname
Scottish
Scottish : habitational name from the lands of Work in the parish of St. Ola, Orkney.English : from Old English (ge)weorc ‘work’, ‘fortification’, hence probably a topographic name or an occupational name for someone who worked on fortifications or at a fort.Danish : habitational name from a place so called.
Girl/Female
Norse Latin
Work.
Girl/Female
Indian, Sikh
Pure Work
Girl/Female
Indian, Sikh
Good Work
Girl/Female
Indian
Intelligence; Work
Boy/Male
Biblical
God's work.
Boy/Male
Tamil
Achievement, Work
Girl/Female
Indian
Good Work
Boy/Male
Hindu
Achievement, Work
Boy/Male
British, English, Indian, Russian
Work
Female
Czechoslovakian
, work.
Female
Croatian
, work.
Boy/Male
British, English, Finnish
Universal; Work
Girl/Female
Biblical
God's work.
Girl/Female
Indian
Hard Work
Boy/Male
Tamil
Effort, Work
Girl/Female
German
Work Ruler
DWORK CONJECTURE
DWORK CONJECTURE
Surname or Lastname
English or Irish
English or Irish : probably a variant of Magnus.Perrygren (Peregrine) Magness was born in 1722 in Britain, and died in 1800 in Warren Co., KY.
Male
Egyptian
, a mystical title of the deity Amen Ra.
Boy/Male
Biblical
My secret.
Boy/Male
Tamil
Lord of seasons, Lord of truth
Boy/Male
Hindu, Indian
To Shine as Bright as the Sun
Boy/Male
Hindu
Peaceful
Boy/Male
Tamil
Karthikeyan
Girl/Female
Arabic, Muslim, Punjabi
Gem; Pearl
Girl/Female
Hebrew American French English
Grace.
Male
Croatian
, soul, spirit.
DWORK CONJECTURE
DWORK CONJECTURE
DWORK CONJECTURE
DWORK CONJECTURE
DWORK CONJECTURE
n.
Specifically: (a) That which is produced by mental labor; a composition; a book; as, a work, or the works, of Addison. (b) Flowers, figures, or the like, wrought with the needle; embroidery.
n.
To make one's way slowly and with difficulty; to move or penetrate laboriously; to proceed with effort; -- with a following preposition, as down, out, into, up, through, and the like; as, scheme works out by degrees; to work into the earth.
n.
The matter on which one is at work; that upon which one spends labor; material for working upon; subject of exertion; the thing occupying one; business; duty; as, to take up one's work; to drop one's work.
v. t.
To labor or operate upon; to give exertion and effort to; to prepare for use, or to utilize, by labor.
v. t.
To influence by acting upon; to prevail upon; to manage; to lead.
n.
Work done by the piece, as in nonmetaliferous rock, the amount done being usually reckoned by the fathom.
v. t.
To cause to ferment, as liquor.
n.
To act or operate on the stomach and bowels, as a cathartic.
n.
Manner of working; management; treatment; as, unskillful work spoiled the effect.
n.
The causing of motion against a resisting force. The amount of work is proportioned to, and is measured by, the product of the force into the amount of motion along the direction of the force. See Conservation of energy, under Conservation, Unit of work, under Unit, also Foot pound, Horse power, Poundal, and Erg.
n.
To ferment, as a liquid.
v. t.
To form with a needle and thread or yarn; especially, to embroider; as, to work muslin.
v. t.
To set in motion or action; to direct the action of; to keep at work; to govern; to manage; as, to work a machine.
v. t.
To produce or form by labor; to bring forth by exertion or toil; to accomplish; to originate; to effect; as, to work wood or iron into a form desired, or into a utensil; to work cotton or wool into cloth.
v. t.
To produce by slow degrees, or as if laboriously; to bring gradually into any state by action or motion.
n.
To be in a state of severe exertion, or as if in such a state; to be tossed or agitated; to move heavily; to strain; to labor; as, a ship works in a heavy sea.
adv.
At work; in action.