In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q.
Let f（z） be a Hecke-Maass cusp form for SL2（Z）, and let L（s, f） be the corresponding automorphic L-function associated to f. For sufficiently large T, let N（σ, T） be the number of zeros p =β ＋ iγ of L（s, ...Let f（z） be a Hecke-Maass cusp form for SL2（Z）, and let L（s, f） be the corresponding automorphic L-function associated to f. For sufficiently large T, let N（σ, T） be the number of zeros p =β ＋ iγ of L（s, f） with ｜γ｜ ≤T, β〉 σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4≤ σ≤ 1 - ε, there exists a constant C = C（ε） such that N（σ, T） 〈〈 T2（1-σ）/σ（log T）c, which improves the previous results.展开更多
§1.IntroductionLet N(σ,T) be the number of zeros of the Riemann zeta funetion ζ(s) in theregion σ≤Re(s)≤1,|Im(s)|≤T.For σ>(3/4),by using the Halász-Montgomerymethod,one can get somo results which a...§1.IntroductionLet N(σ,T) be the number of zeros of the Riemann zeta funetion ζ(s) in theregion σ≤Re(s)≤1,|Im(s)|≤T.For σ>(3/4),by using the Halász-Montgomerymethod,one can get somo results which are better than the classical result givenby Ingham.For example,Jutila proved that the zero density hypothesisN(σ,T)T2-3σ+展开更多
By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the criti...By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.展开更多
We raise and partly answer the question: whether there exists a Markov system with respect to which the zeros of the Chebyshev polynomials are dense, but the maximum length of a zero free interval of the nth Chebyshev...We raise and partly answer the question: whether there exists a Markov system with respect to which the zeros of the Chebyshev polynomials are dense, but the maximum length of a zero free interval of the nth Chebyshev polynomial does not tends to zero. We also draw the conclu- tion that a Markov system, under an additional assumption, is dense if and only if the maxi- mum length of a zero free interval of the nth associated Chebyshev polynomial tends to zero.展开更多
Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actua...Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.展开更多
Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize pe...Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize perfect bending waveguides. According to a coordinate transformation, the surface waves on the input and output interfaces of the ADNZ metamaterial induces the sound energy flow to be redistributed and match smoothly with the propagating modes inside the metamaterial waveguide. According to the theory of bending waveguide, we realize the ＂T＂-type sound shunting and convergence, as well as acoustic channel selection by embedding small-sized defects. Numerical calculations are performed to confirm the above effects.展开更多
基金Supported by the NNSF of China（11071186）Supported by the Science Foundation for the Excellent Youth Scholars of Shanghai（ssc08017）Supported by the Doctoral Research Fund of Shanghai Ocean University
文摘In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q.
基金The author would like to thank Xu Zhao and the referees for carefully reading the manuscript and detailed comments. This work was supported by the National Natural Science Foundation of China （Grant No. 11126151） and the Scientific Foundation of Henan University （Grant No. 2012YBZR030）.
文摘Let f（z） be a Hecke-Maass cusp form for SL2（Z）, and let L（s, f） be the corresponding automorphic L-function associated to f. For sufficiently large T, let N（σ, T） be the number of zeros p =β ＋ iγ of L（s, f） with ｜γ｜ ≤T, β〉 σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4≤ σ≤ 1 - ε, there exists a constant C = C（ε） such that N（σ, T） 〈〈 T2（1-σ）/σ（log T）c, which improves the previous results.
文摘§1.IntroductionLet N(σ,T) be the number of zeros of the Riemann zeta funetion ζ(s) in theregion σ≤Re(s)≤1,|Im(s)|≤T.For σ>(3/4),by using the Halász-Montgomerymethod,one can get somo results which are better than the classical result givenby Ingham.For example,Jutila proved that the zero density hypothesisN(σ,T)T2-3σ+
基金The project supported by National Natural Science Foundation ot China
文摘By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μ<SUB>c</SUB> in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μ<SUB>c</SUB> but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.
文摘We raise and partly answer the question: whether there exists a Markov system with respect to which the zeros of the Chebyshev polynomials are dense, but the maximum length of a zero free interval of the nth Chebyshev polynomial does not tends to zero. We also draw the conclu- tion that a Markov system, under an additional assumption, is dense if and only if the maxi- mum length of a zero free interval of the nth associated Chebyshev polynomial tends to zero.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11275097,11475085,11105122,and 11535005the Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No 1402006C
文摘Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB921504)the National Natural Science Foundation of China(Grant No.11474160)+2 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.020414380001)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.SKLA201609)the Priority Academic Program Development of Jiangsu Higher Education Institution,China
文摘Anisotropic metamaterial with only one component of the mass density tensor near zero （ADNZ） is proposed to control the sound wave propagation. We find that such an anisotropic metamaterial can be used to realize perfect bending waveguides. According to a coordinate transformation, the surface waves on the input and output interfaces of the ADNZ metamaterial induces the sound energy flow to be redistributed and match smoothly with the propagating modes inside the metamaterial waveguide. According to the theory of bending waveguide, we realize the ＂T＂-type sound shunting and convergence, as well as acoustic channel selection by embedding small-sized defects. Numerical calculations are performed to confirm the above effects.
