ON THE ZEROS OF HECKE-TYPE FABER POLYNOMIALS
نویسندگان
چکیده
منابع مشابه
The zeros of Faber polynomials generated by an m-star
It is shown that the zeros of the Faber polynomials generated by a regular m-star are located on the m-star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.
متن کاملZeros of the derivatives of Faber polynomials associated with a universal covering map
For a compact set E ⊂ C containing more than two points, we study asymptotic behavior of normalized zero counting measures {μk} of the derivatives of Faber polynomials associated with E. For example if E has empty interior, we prove that {μk} converges in the weakstar topology to a measure whose support is the boundary of g(D), where g : {|z| > r} ∪ {∞} → C\E is a universal covering map such th...
متن کاملOn the Zeros of Polynomials with Littlewood-type Coefficient Constraints
For z0 ∈ C and r > 0, let D(z0, r) := {z ∈ C : |z − z0| < r} . In this paper we show that a polynomial p of the form
متن کاملZeros and Local Extreme Points of Faber Polynomials Associated with Hypocycloidal Domains∗
Faber polynomials play an important role in different areas of constructive complex analysis. Here, the zeros and local extreme points of Faber polynomials for hypocycloidal domains are studied. For this task, we use tools from linear algebra, namely, the Perron-Frobenius theory of nonnegative matrices, the Gantmacher-Krein theory of oscillation matrices, and the Schmidt-Spitzer theory for the ...
متن کاملOn the irreducibility of Hecke polynomials
Let Tn,k(X) be the characteristic polynomial of the nth Hecke operator acting on the space of cusp forms of weight k for the full modular group. We record a simple criterion which can be used to check the irreducibility of the polynomials Tn,k(X). Using this criterion with some machine computation, we show that if there exists n ≥ 2 such that Tn,k(X) is irreducible and has the full symmetric gr...
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: Kyushu Journal of Mathematics
سال: 2008
ISSN: 1340-6116
DOI: 10.2206/kyushujm.62.15