Proof of the Sendov conjecture for polynomials of degree nine
In this paper, we prove the Sendov conjecture for polynomials of degree nine. We use a new idea to obtain new upper bound for the $σ-$sum to zeros of the polynomial.
math.CV↗
arXiv subjects
Zaizhao Meng
Publications and source records attributed to Zaizhao Meng.
Inequalities for Continued Fractions, II
In this paper, we investigate the monotone property of the continued fractions $G(m,λ)$ as a function of $m$ and $λ$. In particular, we obtain new inequality for the relative continued fractions.
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On the Sendov conjecture and the critical points of polynomials
In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.
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The critical points of a polynomial
In this paper, we obtain new results on the critical points of a polynomial, these results are useful to the Sendov conjecture.
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A Note on the Linnik's constant
Let $P(a,q)$ be the least prime in the arithmetic progression $\{n\equiv a(mod\ q)\}$. In this note, when $q$ has bounded cubic part and $(a,q)=1$, we combine the Heath-Brown's method and the Burgess's bounds for L-functions to obtain $ P(a,q)\ll q^{4.5}.$
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On a variance for twins of $k-$free numbers in arithmetic progressions
In this paper, we give a new upper bound of Barban-Davenport-Halberstam type for twins of $k-$free numbers in arithmetic progressions.
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