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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Zeros of complete symmetric polynomials over finite fields
有限域 完全对称 多项式 零点
2023/4/13
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Siegel Zeros and Applications
西格尔零点 Landau-Siegel零点 大黎曼猜想 狄利克雷L函数
2023/4/24
Siegel zeros are real zeros of L-functions that are very close to 1, the non-existence of which was conjectured as a direct consequence of the Grand Riemann Hypothesis (GRH). In this talk, we will sta...
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann’s zeta function
Statistical tests random unitary matrix Riemann zeta function data set
2015/7/14
This paper presents some new statistical tests and new conjectures regarding
the correspondence between the eigenvalues of random unitary matrices and
the zeros of Riemann’s zeta function. Global fe...
Distribution of Zeros of Mittag-Leffler Function and Relevant Spectrum Analysis
Eigenvalue of Operator Fractional Derivative Mittag-LefflerFunction Spectrum Analysis
2012/8/10
This paper is devoted to the distribution of eigenvalues of op-
erators generated by differential expressions of fractional order with Sturm-
Liouville regional conditions. In particular it offers a...
Distinct zeros and simple zeros of Dirichlet $L$-functions
simple zeros distinct zeros Dirichlet L-function
2012/6/29
We study the number of distinct zeros and simple zeros of Dirichlet $L$-function by using Asymptotic Large Sieve in this paper. In asymptotic terms, we prove that there are more than 66.43% of zeros o...
Random determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields
Gaussian random determinant Wishart matrix Gaussian random parallelotope mixed volumes of ellipsoids location-dispersion ellipsoid
2012/6/15
Consider a $d\times d$ matrix $M$ whose rows are independent centered non-degenerate Gaussian vectors $\xi_1,...,\xi_d$ with covariance matrices $\Sigma_1,...,\Sigma_d$. Denote by $\mathcal{E}_i$ the ...
Entire Functions of Exponential-Type with Given Zeros
Entire functions Exponential-type Zeros the Growth
2011/10/20
In this paper, we consider some entire functions of exponential-type with given zeros, a kind of sequences of complex numbers in the right half-plane, and discuss the growth of the functions on the im...
Lee-Yang-Fisher zeros for DHL and 2D rational dynamics, II. Global Pluripotential Interpretation
Lee-Yang-Fisher zeros 2D rational dynamics Global Pluripotential Interpretation
2011/9/22
Abstract: In a classical work of the 1950's, Lee and Yang proved that for fixed nonnegative temperature, the zeros of the partition functions of a ferromagnetic Ising model always lie on the unit circ...
Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials
Stokes and Navier–Stokes equations in R3 blow-up scaling solenoidal Hermite polynomials eigenfunction expansion
2011/9/9
Abstract: Multiple spatial zero formations for Stokes and Navier-Stokes equations in three dimensions are shown to occur according to nodal sets of solenoidal Hermite polynomials. Extensions to well-p...
Trivial zeros of p-adic L-functions at near central points
Trivial zeros p-adic L-functions central points Number Theory
2011/8/26
Abstract: Using the $\scr L$-invariant constructed in our previous paper we prove a Mazur-Tate-teitelbaum style formula for derivatives of p-adic L-functions at near central points.
Some results on zeros distributions and uniqueness of derivatives of difference polynomials
Zeros difference polynomials derivatives value sharing uniqueness
2011/8/25
Abstract: We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conj...
In this paper, we prove some extensions and generalizations of the classical Eneström-Kakeya theorem.
Subordination by orthogonal martingales in $L^{p}$ and zeros of Laguerre polynomials
orthogonal martingales $L^{p}$ zeros of Laguerre polynomials
2011/1/18
In this paper we address the question of finding the best Lp-norm constant for martingale transforms with one-sided orthogonality. Let O = (,B, P)be a probability space with filtration B generated by ...
On the zeros of Weng zeta functions for Chevalley groups
Weng zeta functions Chevalley groups
2010/11/23
We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over $\Q$ are simple and on the critical line.
Zeros of nonpositive type of generalized Nevanlinna functions with one negative square
Nevanlinna functions negative square
2010/11/15
A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation d...