Evenly Divisible Rational Approximations of Quadratic Irrationalities
| Autor: | Dan Carmon |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematics::Dynamical Systems
Mathematics - Number Theory Approximations of π General Mathematics Mathematics::Number Theory 010102 general mathematics Of the form 0102 computer and information sciences 01 natural sciences Combinatorics Quadratic equation 010201 computation theory & mathematics FOS: Mathematics Quadratic irrational Number Theory (math.NT) 0101 mathematics Algebra over a field Dynamical billiards Laplace operator 11B39 11J68 11R11 11R80 Eigenvalues and eigenvectors Mathematics |
| Popis: | In a recent paper of Blomer, Bourgain, Radziwi{\l}{\l} and Rudnick, the authors proved the existence of small gaps between eigenvalues of the Laplacian in a rectangular billiard with sides $\pi$ and $\pi/\sqrt\alpha$, i.e. numbers of the form $\alpha m^2+ n^2$, whenever $\alpha$ is a quadratic irrationality of certain types. In this note, we extend their results to all positive quadratic irrationalities $\alpha$. Comment: 7 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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