Integral Points on the Unit Circle
نویسندگان
چکیده
منابع مشابه
On the Unit Circle
New characterizations are given for orthogonal polynomials on the unit circle and the associated measures in terms of the reflection coefficients in the recurrence equation satisfied by the polynomials.
متن کاملThere Are Integral Heptagons, no Three Points on a Line, no Four on a Circle
We give two configurations of seven points in the plane, no three points in a line, no four points on a circle with pairwise integral distances. This answers a famous question of Paul Erd˝ os.
متن کاملMass Points of Measures and Orthogonal Polynomials on the Unit Circle
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szegő recurrences. We assume that the reflection coefficients tend to some complex number a with 0 < |a| < 1. The orthogonality measure μ then lives essentially on the arc {e : α ≤ t ≤ 2π − α} where sin α 2 def = |a| with α ∈ (0, π). Under the certain rate of convergence it was prove...
متن کاملSynthesis by Arcs on the Unit Circle
Take a set of n arcs on the unit circle and consider the characteristic function of the set of n arcs. Think of this as a waveform, taking only the values 0 and 1. Produce a sound by generating a wavetable by sample and hold. You can think of this procedure as a very simple synthesizer. The question is: which sounds can be generated in this way. The surprising answer is: all of them. Thanks to ...
متن کاملWeighted Energy Problem on the Unit Circle
We solve the weighted energy problem on the unit circle by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also included.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2001
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2635