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Search Results: 1 - 10 of 131416 matches for " Li Xian "
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Reconstruction in time-warped weighted shift-invariant spaces with application to spline subspaces
Jun Xian,Yongjin Li
International Journal of Mathematics and Mathematical Sciences , 2003, DOI: 10.1155/s0161171203212126
Abstract: We discuss the reproducing kernel structure in shift-invariant spaces and the weighted shift-invariant spaces, and obtain the reconstruction formula in time-warped weighted shift-invariant spaces, then apply them to a spline subspace. In the spline subspace, we give a reconstruction formula in a time-warped spline subspace.
Primary Study on Correlation Dimension of 24h HRV in Different Frequency Domains
Xia Li,Xian Xu
Lecture Notes in Engineering and Computer Science , 2009,
Abstract:
{N-Methyl-N′-[1-(pyridin-2-yl)ethylidene]ethane-1,2-diamine-κ3N,N′,N′′}bis(thiocyanato-κN)zinc(II)
Xian-Wen Li
Acta Crystallographica Section E , 2011, DOI: 10.1107/s1600536811019945
Abstract: In the title compound, [Zn(NCS)2(C10H15N3)], the Zn atom is five-coordinated by the three N-donor atoms of the Schiff base ligand and by two N atoms from two thiocyanate anions, forming a distorted ZnN5 trigonal–bipyramidal coordination geometry for the metal ion. The side chain of the ligand is disordered over two sets of sites in a 0.655 (12):0.345 (12) ratio. In the crystal, molecules are linked by N—H...S hydrogen bonds, generating [100] chains.
A residue scalar product for algebraic function fields over a number field
Xian-Jin Li
Mathematics , 1999,
Abstract: In 1952 Peter Roquette gave an arithmetic proof of the Riemann hypothesis for algebraic function fields of a finite constants field, which was proved by Andr\'e Weil in 1940. The construction of Weil's scalar product is essential in Roquette's proof. In this paper a scalar product for algebraic function fields over a number field is constructed which is the analogue of Weil's scalar product.
On the trace of Hecke operators for Maass forms for congruence subgroups II
Xian-Jin Li
Mathematics , 2001,
Abstract: Let E_lambda be the Hilbert space spanned by the eigenfunctions of the non-Euclidean Laplacian associated with a positive discrete eigenvalue lambda. In this paper, the trace of Hecke operators T_n acting on the space E_lambda is computed for Hecke congruence subgroups Gamma_0(N) of non-square free level. This extends the computation of Conrey-Li [2], where only Hecke congruence subgroups Gamma_0(N) of square free level N were considered.
A proof of the Riemann hypothesis
Xian-Jin Li
Mathematics , 2008,
Abstract: This paper has been withdrawn by the author, due to a mistake on page 29.
On exceptional eigenvalues of the Laplacian for $Γ_0(N)$
Xian-Jin Li
Mathematics , 2006,
Abstract: An explicit Dirichlet series is obtained, which represents an analytic function of $s$ in the half-plane $\Re s>1/2$ except for having simple poles at points $s_j$ that correspond to exceptional eigenvalues $\lambda_j$ of the non-Euclidean Laplacian for Hecke congruence subgroups $\Gamma_0(N)$ by the relation $\lambda_j=s_j(1-s_j)$ for $j=1,2,..., S$. Coefficients of the Dirichlet series involve all class numbers $h_d$ of real quadratic number fields. But, only the terms with $h_d\gg d^{1/2-\epsilon}$ for sufficiently large discriminants $d$ contribute to the residues $m_j/2$ of the Dirichlet series at the poles $s_j$, where $m_j$ is the multiplicity of the eigenvalue $\lambda_j$ for $j=1,2,..., S$. This may indicate (I'm not able to prove yet) that the multiplicity of exceptional eigenvalues can be arbitrarily large. On the other hand, by density theorem [3] the multiplicity of exceptional eigenvalues is bounded above by a constant depending only on $N$.
A note on zeros of $L$-series of elliptic curves
Xian-Jin Li
Mathematics , 2006,
Abstract: In this note we study an analogy between a positive definite quadratic form for elliptic curves over finite fields and a positive definite quadratic form for elliptic curves over the rational number field. A question is posed of which an affirmative answer would imply the analogue of the Riemann hypothesis for elliptic curves over the rational number field.
An explicit formula for Hecke $L$-functions
Xian-Jin Li
Mathematics , 2004,
Abstract: In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of Hecke polynomials, which are associated with the space of cusp forms of weight $k$ for Hecke congruence subgroups, lie on the critical line.
An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
Xian-Jin Li
Mathematics , 2004,
Abstract: In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias obtained an arithmetic formula for these coefficients using the ``explicit formula'' of prime number theory. In this paper, the author obtains an arithmetic formula for corresponding coefficients associated with the Euler product of Hecke polynomials, which is essentially a product of L-functions attached to weight 2 cusp forms (both newforms and oldforms) over Hecke congruence subgroups. The nonnegativity of these coefficients gives a criterion for the Riemann hypothesis for all these L-functions at once.
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