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- Mahler's_theorem abstract "In mathematics, Mahler's theorem, introduced by Kurt Mahler (1958), expresses continuous p-adic functions in terms of polynomials.In any field, one has the following result. Letbe the forward difference operator. Then for polynomial functions f we have the Newton series:whereis the kth binomial coefficient polynomial.Over the field of real numbers, the assumption that the function f is a polynomial can be weakened, but it cannot be weakened all the way down to mere continuity.Mahler's theorem states that if f is a continuous p-adic-valued function on the p-adic integers then the same identity holds.The relationship between the operator Δ and this polynomial sequence is much like that between differentiation and the sequence whose kth term is xk.It is remarkable that as weak an assumption as continuity is enough; by contrast, Newton series on the complex number field are far more tightly constrained, and require Carlson's theorem to hold. It is a fact of algebra that if f is a polynomial function with coefficients in any field of characteristic 0, the same identity holds where the sum has finitely many terms.".
- Mahler's_theorem wikiPageExternalLink purl?GDZPPN002177846.
- Mahler's_theorem wikiPageID "408111".
- Mahler's_theorem wikiPageRevisionID "543742614".
- Mahler's_theorem authorlink "Kurt Mahler".
- Mahler's_theorem first "Kurt".
- Mahler's_theorem hasPhotoCollection Mahler's_theorem.
- Mahler's_theorem last "Mahler".
- Mahler's_theorem year "1958".
- Mahler's_theorem subject Category:Factorial_and_binomial_topics.
- Mahler's_theorem subject Category:Theorems_in_analysis.
- Mahler's_theorem type Abstraction100002137.
- Mahler's_theorem type Communication100033020.
- Mahler's_theorem type Message106598915.
- Mahler's_theorem type Proposition106750804.
- Mahler's_theorem type Statement106722453.
- Mahler's_theorem type Theorem106752293.
- Mahler's_theorem type TheoremsInAnalysis.
- Mahler's_theorem comment "In mathematics, Mahler's theorem, introduced by Kurt Mahler (1958), expresses continuous p-adic functions in terms of polynomials.In any field, one has the following result. Letbe the forward difference operator.".
- Mahler's_theorem label "Mahler's theorem".
- Mahler's_theorem label "Théorème de Mahler".
- Mahler's_theorem label "マーラーの定理".
- Mahler's_theorem sameAs Théorème_de_Mahler.
- Mahler's_theorem sameAs マーラーの定理.
- Mahler's_theorem sameAs m.024q4f.
- Mahler's_theorem sameAs Q3527118.
- Mahler's_theorem sameAs Q3527118.
- Mahler's_theorem sameAs Mahler's_theorem.
- Mahler's_theorem wasDerivedFrom Mahler's_theorem?oldid=543742614.
- Mahler's_theorem isPrimaryTopicOf Mahler's_theorem.