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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26. 相似文献
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This paper concerns a Markov operator T on a space L1, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:
- a the existence of invariant probabilitydensities (IPDs)
- b the existence of strictly positive IPDs,and
- c the existence and uniqueness of IPDs.
- b the existence of strictly positive IPDs,and
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应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统. 相似文献
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We have deposited relatively thick (∼60 nm) Ge layers on Br-passivated Si(111) substrates by thermal evaporation under high
vacuum conditions at room temperature. Ge has grown in a layer-plus-island mode although it is different from the Stranski-Krastanov
growth mode observed in epitaxial growth. Both the islands and the layer are nanocrystalline. This appears to be a consequence
of reduction of surface free energy of the Si(111) substrate by Br-passivation. The size distribution of the Ge nanoislands
has been determined. The Br-Si(111) substrates were prepared by a liquid treatment, which may not produce exactly reproducible
surfaces. Nevertheless, some basic features of the nanostructural island growth are reasonably reproducible, while there are
variations in the details of the island size distribution. 相似文献
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JB Pendry 《Contemporary Physics》2013,54(3):191-202
Light bends the wrong way in materials where both ε and μ are negative as was pointed out in 1968, but the absence of natural materials with this property led to neglect of the subject until 1999 when it was shown how to make artificial materials, metamaterials, with negative μ. The rapid advance of the subject since that date, both in theory and experiment, is reflected in the exponential growth of publications now at the 200 per year level and still growing. This interest is explained by the sudden availability of a qualitatively different class of electromagnetic materials combined with the quite startling properties which these materials appear to have; all of which provokes debate as each new facet of their behaviour is revealed. Experiment has been vital to resolution of controversy and has chiefly been in the microwave region of the spectrum though there is potential in the optical region currently being explored by several groups. 相似文献
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G Viesti M Lunardon D Fabris G Nebbia M Cinausero E Fioretto G Prete JB Natowitz K Hagel R Wada 《Pramana》1999,53(3):395-404
The transition of the level density parameter a
off from the low excitation energy value a
off=A/8 MeV−1 to the Fermi gas value a
FG ∼ A/15 MeV−1 was discovered a few years ago studying particle spectra evaporated from hot compound systems of A∼ 160. A number of experiments have been recently performed to confirm the earlier findings and extend the investigation to
other mass regions and to higher excitation energies. Furthermore, precision coincidence experiments have been done in the
lead region in which evaporation residues are tagged by low energy gammarays. Those experiments open the possibility of a
detailed study of the level densities in nuclei where the shell effects are important. 相似文献
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