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121.
The summatory function of the Möbius function is denotedM(x). In this article we deduce conditional results concerningM(x) assuming the Riemann hypothesis and a conjecture of Gonekand Hejhal on the negative moments of the Riemann zeta function.Assuming these conjectures, we show that M(x), when appropriatelynormalized, possesses a limiting distribution, and also thata strong form of the weak Mertens conjecture is true. Finally,we speculate on the lower order of M(x) by studying the constructeddistribution function. 2000 Mathematics Subject Classification11M26, 11N56. 相似文献
122.
123.
Mohd Mustapa MF Harris R Esposito D Chubb NA Mould J Schultz D Driscoll PC Tabor AB 《The Journal of organic chemistry》2003,68(21):8193-8198
Two diastereomeric analogues of ring C of nisin incorporating a novel norlanthionine residue have been synthesized via a triply orthogonal protecting group strategy. A full structural study was carried out by NMR, which elucidated the conformational properties of the two peptides and enabled the identity of each diastereoisomer to be proposed. 相似文献
124.
125.
Nathan L. Harshman 《International Journal of Theoretical Physics》2007,46(8):1929-1946
The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for
this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge
from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré
group. 相似文献
126.
Nathan Keller 《Journal of Combinatorial Theory, Series A》2010,117(4):389-410
In Kalai (2002) [10], Kalai investigated the probability of a rational outcome for a generalized social welfare function (GSWF) on three alternatives, when the individual preferences are uniform and independent. In this paper we generalize Kalai's results to a broader class of distributions of the individual preferences, and obtain new lower bounds on the probability of a rational outcome in several classes of GSWFs. In particular, we show that if the GSWF is monotone and balanced and the distribution of the preferences is uniform, then the probability of a rational outcome is at least 3/4, proving a conjecture raised by Kalai. The tools used in the paper are analytic: the Fourier-Walsh expansion of Boolean functions on the discrete cube, properties of the Bonamie-Beckner noise operator, and the FKG inequality. 相似文献
127.
128.
N. Linial 《Combinatorica》1986,6(1):49-54
The following computational problem was initiated by Manber and Tompa (22nd FOCS Conference, 1981): Given a graphG=(V, E) and a real functionf:V→R which is a proposed vertex coloring. Decide whetherf is a proper vertex coloring ofG. The elementary steps are taken to be linear comparisons.
Lower bounds on the complexity of this problem are derived using the chromatic polynomial ofG. It is shown how geometric parameters of a space partition associated withG influence the complexity of this problem.
Existing methods for analyzing such space partitions are suggested as a powerful tool for establishing lower bounds for a
variety of computational problems. 相似文献
129.
Nathan Ng 《Journal of Number Theory》2008,128(3):509-556
We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the zeta function whose spacing is three times larger than the average spacing. This is deduced from the calculation of the second moment of the Riemann zeta function multiplied by a Dirichlet polynomial averaged over the zeros of the zeta function. 相似文献
130.
Assuming the Riemann hypothesis, we exhibit large and smallvalues of the derivative of the zeta function evaluated at thenon-trivial zeros of the zeta function. These results are provedby applying Soundararajan's resonance method. 相似文献