Around a Conjecture of K. Tran
| Autor: | Ndikubwayo, Innocent |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the root distribution of a sequence of polynomials $\{P_n(z)\}_{n=0}^{\infty}$ with the rational generating function $$ \sum_{n=0}^{\infty} P_n(z)t^n= \frac{1}{1+ B(z)t^\ell +A(z)t^k}$$ for $(k,\ell)=(3,2)$ and $(4,3)$ where $A(z)$ and $B(z)$ are arbitrary polynomials in $z$ with complex coefficients. We show that the zeros of $P_n(z)$ which satisfy $A(z)B(z)\neq 0$ lie on a real algebraic curve which we describe explicitly. Comment: 23 pages, 10 figures |
| Databáze: | arXiv |
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