scholarly journals The representation of integers by positive ternary quadratic polynomials

2015 ◽  
Vol 156 ◽  
pp. 75-94 ◽  
Author(s):  
Wai Kiu Chan ◽  
James Ricci
Keyword(s):  
Quadratic Polynomials ◽  
Representation Of Integers

scholarly journals Distribution of polynomials with cycles of a given multiplier

2011 ◽  
Vol 201 ◽  
pp. 23-43 ◽  
Author(s):  
Giovanni Bassanelli ◽  
François Berteloot
Keyword(s):  
Quadratic Polynomials ◽  
Bifurcation Locus

AbstractIn the space of degreedpolynomials, the hypersurfaces defined by the existence of a cycle of periodnand multipliereiθare known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.

A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers

2008 ◽  
Vol 15 (1) ◽  
pp. 189-194
Author(s):  
Ahmad Zireh
Keyword(s):  
Mandelbrot Set ◽  
Complex Numbers ◽  
Quadratic Polynomials ◽  
Bicomplex Numbers

Abstract We use a commutative generalization of complex numbers called bicomplex numbers to introduce the bicomplex dynamics of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑤) = 𝑤(𝑤 + 𝑐)𝑑. Rochon [Fractals 8: 355–368, 2000] proved that the Mandelbrot set of quadratic polynomials in bicomplex numbers of the form 𝑤2 + 𝑐 is connected. We prove that our generalized Mandelbrot set of polynomials of type 𝐸𝑑, 𝑓𝑐(𝑤) = 𝑤(𝑤 + 𝑐)𝑑, is connected.

On the representation of integers as sums of triangular numbers

1995 ◽  
Vol 50 (1-2) ◽  
pp. 73-94 ◽  
Author(s):  
Ken Ono ◽  
Sinai Robins ◽  
Patrick T. Wahl
Keyword(s):  
Triangular Numbers ◽  
Representation Of Integers

Quadratic Polynomials

1993 ◽  
pp. 123-159
Author(s):  
Lennart Carleson ◽  
Theodore W. Gamelin
Keyword(s):  
Quadratic Polynomials
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