In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin (1969) in deformation theory which implies that formal power series...

category of schemes has led to the Artin approximation theorem in local algebra as well as the "Existence theorem". This work also gave rise to the ideas...

mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate...

mathematics, the Artin–Rees lemma is a basic result about modules over a Noetherian ring, along with results such as the Hilbert basis theorem. It was proved...

(algebra) Strassmann's theorem (field theory) Sturm's theorem (theory of equations) Vieta's formulas (quadratics) Artin approximation theorem (commutative algebra)...

completion of A. The notion of the approximation property is due to Michael Artin. Artin approximation theorem Popescu's theorem Rotthaus, Christel (1997). "Excellent...

provided by Richard Swan. The usual proof of the Artin approximation theorem relies crucially on Popescu's theorem. Popescu's result was proved by an alternate...

X\times _{F}Y\to Y} is smooth and surjective. Artin approximation theorem Schlessinger's theorem Artin, M. (September 1974). "Versal deformations and...

Binomial distribution Binomial inverse theorem Binomial coefficient Stirling's approximation Tannery's theorem Polynomials calculating sums of powers...

Dedekind zeta functions factorize as a product of powers of Artin L-functions, so zeros of Artin L-functions sometimes give rise to multiple zeros of Dedekind...

theorem itself was famously applied by Michael Artin and Barry Mazur to the study of dynamical systems, by combining Nash's polynomial approximation together...

Springer. ISBN 3-540-41160-7. Bronshteĭn & Semendiaev 1971, pp. 191–192. Artin, Emil (1964). The Gamma Function. Athena series; selected topics in mathematics...

algebraization question, and has been largely put on a firm basis by Artin's approximation theorem. A formal universal deformation is by definition a formal scheme...

(mathematics), Eben Matlis; Dualizing module, Popescu's theorem, Artin approximation theorem. This notion can be related to the spectrum of a linear operator;...

Prize Emil Artin Solved Hilbert's seventeenth problem partially solved Hilbert's ninth problem Michael Artin Artin approximation theorem Algebraic spaces...

a complete local ring. This object can be approximated via Artin's approximation theorem by an object defined over a finitely generated ring. The spectrum...

Polygamma function q-gamma function Ramanujan's master theorem Spouge's approximation Stirling's approximation Davis, P. J. (1959). "Leonhard Euler's Integral:...

theorem holds are conservative systems; thus all ergodic systems are conservative. More precise information is provided by various ergodic theorems which...

Vienna, was descended from an Armenian carpet merchant. Artin, Michael (1969), "Algebraic approximation of structures over complete local rings", Publications...

Teiji Takagi. Emil Artin established the Artin reciprocity law in a series of papers (1924; 1927; 1930). This law is a general theorem in number theory...

Taylor approximation, established an approximation of differentiable functions f {\displaystyle f} by polynomials. By the Stone–Weierstrass theorem, every...

Riches to Raags: 3-Manifolds, Right-Angled Artin Groups, and Cubical Geometry: 3-manifolds, Right-angled Artin Groups, and Cubical Geometry. American Mathematical...

Strzelecki, Michał (2022). "Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings". Journal of Approximation Theory. 277: 105736. arXiv:2103...

as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...

abelian varieties See main article arithmetic of abelian varieties Artin L-functions Artin L-functions are defined for quite general Galois representations...

formula Artin conjecture Sato–Tate conjecture Langlands program modularity theorem Pythagorean triple Pell's equation Elliptic curve Nagell–Lutz theorem Mordell–Weil...

such as Siegel's theorem on integral points, come from the theory of diophantine approximation. The basic result, the Mordell–Weil theorem in Diophantine...

has played a role in proving many cases of Artin's conjecture and in Wiles's proof of Fermat's Last Theorem. The left-hand side of Eq.1 becomes a sum over...

Pierre Deligne. Collaborators on the SGA projects also included Michael Artin (étale cohomology), Nick Katz (monodromy theory, and Lefschetz pencils)...

he published the Stone–Weierstrass theorem which generalized Weierstrass's theorem on the uniform approximation of continuous functions by polynomials...