Diophantine Approximation
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Home > Art, Film & Photography > Diophantine Approximation: Liouville Number, Auxiliary Function, Low-Discrepancy Sequence, Beatty Sequence, Discrepancy of Hypergraphs
Diophantine Approximation: Liouville Number, Auxiliary Function, Low-Discrepancy Sequence, Beatty Sequence, Discrepancy of Hypergraphs

Diophantine Approximation: Liouville Number, Auxiliary Function, Low-Discrepancy Sequence, Beatty Sequence, Discrepancy of Hypergraphs


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 25. Chapters: Liouville number, Auxiliary function, Low-discrepancy sequence, Beatty sequence, Discrepancy of hypergraphs, Markov number, Schneider-Lang theorem, Equidistributed sequence, Thue-Siegel-Roth theorem, Oppenheim conjecture, Equidistribution theorem, Restricted partial quotients, Harmonious set, Littlewood conjecture, Kronecker's theorem, Siegel's lemma, Proof that e is irrational, Discrepancy theory, Markov spectrum, Weyl's inequality, Davenport-Schmidt theorem, Lagrange number, Dirichlet's approximation theorem, Van der Corput sequence, Subspace theorem, Constructions of low-discrepancy sequences, Hurwitz's theorem, Duffin-Schaeffer conjecture, Weyl's criterion, Auxiliary polynomial theorem. Excerpt: 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 are not a rigorously defined kind of function, rather they are functions which are either explicitly constructed or at least shown to exist and which provide a contradiction to some assumed hypothesis, or otherwise prove the result in question. Creating a function during the course of a proof in order to prove the result is not a technique exclusive to transcendence theory, but the term "auxiliary function" usually refers to the functions created in this area. Because of the naming convention mentioned above, auxiliary functions can be dated back to their source simply by looking at the earliest results in transcendence theory. One of these first results was Liouville's proof that transcendental numbers exist when he showed that the so called Liouville numbers were transcendental. He did this...


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Product Details
  • ISBN-13: 9781156440902
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Weight: 68 gr
  • ISBN-10: 1156440904
  • Publisher Date: 29 Aug 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Liouville Number, Auxiliary Function, Low-Discrepancy Sequence, Beatty Sequence, Discrepancy of Hypergraphs
  • Width: 189 mm


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