Number Theory Seminar

Presented by: Karl Dilcher

Title: “Zeros and irreducibility of some classes of special polynomials”


In the first part of this talk I will define a sequence of polynomials resembling the Chebyshev polynomials of the first kind, and present results on their irreducibility and zero distribution. I will also consider $2\times 2$ Hankel determinants of these polynomials, which have interesting zero distributions. Furthermore, if these polynomials are split into two halves, then the zeros of one half lie in the interval $(-1,1)$, while those of the other half lie on the unit circle.

If time allows, I will also talk about various other number theoretic polynomials, in particular polynomials with gcd powers a coefficients, and once again consider their irreducibility and zero distribution.


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#319 Colloquium Room, Chase Building