the convergence exponent of the zeros of an entire function, the Jensen inequality for the counting function, the Cauchy theorem on the comparison of the zeros of polynomials, Ostrowski's inequalities for the real and imaginary parts of the zeros of polynomials and the Cartwright–Levinson theorem...
24:07 Lambert series of logarithm and a mean value theorem for ζ(12−it)ζ′(12+it) 29:04 Negative moments of the Riemann zeta function 53:21 One-level density of zeros of Dirichlet L-functions over function fields 25:38 A moment with L-functions 59:07 The recipe for moments of ...
The authors give rather complicated lower bounds R 2 and R 4 , corresponding to R 1 and R 3 , producing annular regions R 2 ≤|z|≤R 1 (Theorem 1) and R 4 ≤|z|≤R 3 (Theorem 2) containing all the zeros of f. They claim that, in case k=0 or k=n-1, these give ...
Stieltjes' TheoremLaguerre polynomialsQuasi-orthogonal polynomialsWe discuss interlacing properties of zeros of Laguerre polynomials of different degree in quasi-orthogonal sequences {L-n((alpha))}(n=0)(infinity) characterized by -2 < alpha < -1. Interlacing of zeros of L-n((alpha)...
The main purpose of this paper is to consider the differential equation $u^{(m)}=P(z)u$ $(m\geq 2)$ where $P$ is a polynomial with in general complex coefficients. Let $z_{k}(u),$ $k=1,2,\ldots$ be the zeros of a nonzero solution $u$ to that equation. We obtain bo...
Our investigation extends previous results on small zeros of quadratic forms, including Cassels' theorem and its various generalizations and contributes to the literature of so-called "absolute" Diophantine results with respect to height. All bounds on height are explicit. 展开 ...
It can be visualized by l×y matrix M=(mi,j) of zeros and ones called Ferrers matrix for x and defined by a sum of its row vector r(M)=x and the properties: (1) y≥l, (2) if mi,j=0 then mi,t=0 for all t≥j. In our concept modified Ferrers matrix is also defined by...
bounds. Bounds for monotonic systems withdn(x)en(x) < 0 are also given, in particular for Hermite and Laguerre polynomials of real positive variable; in that case the bounds can be used for bounding the monotonic region (and then the extreme zeros)....
Resonance are defined as zeros of a Fredholm determinant on a non-physical sheet of three sheeted Riemann surface. We determine upper bounds of the ... EL Korotyaev - 《Journal of Mathematical Analysis & Applications》 被引量: 0发表: 2019年 加载更多来源...
LOCI OF COMPLEX POLYNOMIALS, PART I. The classical Grace theorem states that every circular domain in the complex plane C containing the zeros of a polynomial p(z) contains a zero of any of it... SENDOV,BLAGOVEST,HRISTO - 《Transactions of the American Mathematical Society》 被引量: 2发表...