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Auxiliary function

In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions that appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value zero for many arguments, or having a zero of high order at some point.

Auxiliary functions from the pigeonhole principle, Explicit functions & Interpolation determinants

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Explicit functions

Auxiliary functions from the pigeonhole principle

Interpolation determinants

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Auxiliary function

Nodes45
Edges44
Triples64
Avg. degree1.96
Density0.044444
Components1

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Auxiliary function

Top relations

related to Auxiliary functions from the pigeonhole principle · 16
Auxiliary function → Alan Baker, Alexander Gelfond, Another, Axel Thue, Baker's, Carl Ludwig Siegel, Gelfond, Moreover, Pigeonhole Principle Thue, Schneider, Siegel, The, Their, Theodor Schneider, This, Using
related to A theorem of Lang · 15
Auxiliary function → Because, But, Gelfond, Hermite, In, Lang, Lindemann, Schneider, Serge Lang, Siegel's, The, This, To, Under, Using
related to Liouville's transcendence criterion · 9
Auxiliary function → Because, He, Liouville, Liouville's, One, Specifically, The, This, To
related to Hermite's proof of the transcendence of e · 7
Auxiliary function → Ak, By, For, Hermite, Multiplying, Rk, To
related to Interpolation determinants · 7
Auxiliary function → After, Arakelov, Jean-Benoît Bost, Michel Laurent, Since, The, These
related to Fourier's proof of the irrationality of e · 4
Auxiliary function → Another, By, Fourier's, Specifically
related to Hermite's proof of the irrationality of er · 4
Auxiliary function → But, Fourier, Hermite, In
related to Definition · 2
Auxiliary function → Auxiliary, Creating

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Important terminology

functions auxiliary function number polynomial hermite theorem algebraic order rational using value used transcendental transcendence proof lang prove result numbers

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Auxiliary functionrelated to A theorem of LangIn0.60section
Auxiliary functionrelated to A theorem of LangSerge Lang0.60section
Auxiliary functionrelated to A theorem of LangThe0.60section
Auxiliary functionrelated to A theorem of LangHermite0.60section
Auxiliary functionrelated to A theorem of LangLindemann0.60section
Auxiliary functionrelated to A theorem of LangGelfond0.60section
Auxiliary functionrelated to A theorem of LangSchneider0.60section
Auxiliary functionrelated to A theorem of LangUnder0.60section
Auxiliary functionrelated to A theorem of LangTo0.60section
Auxiliary functionrelated to A theorem of LangLang0.60section
Auxiliary functionrelated to A theorem of LangThis0.60section
Auxiliary functionrelated to A theorem of LangBut0.60section

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