On the Möbius function

Maier, Helmut

doi:10.1090/s0002-9947-1987-0882708-5

Cited by 6 publications

(6 citation statements)

References 9 publications

(3 reference statements)

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“…Remerciements. Les auteurs prennent plaisirà remercier ici Helmut Maier pour son aide lors de l'élaboration de cet article, notamment la vérification que sa preuve du résultat principal de [12] s'adapte sans difficulté au cas d'un caractère de Dirichlet réel et non principal.…”

Section: •2 Applicationśunclassified

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Oscillations localisées sur les diviseurs

Bretèche¹,

Tenenbaum²

2012

Journal of the London Mathematical Society

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Section: •2 Applicationśunclassified

“…tendent ou non vers l'infini avec x. La réponse est positive : Maier a en e↵etétabli dans [12] que l'on a, pour presque tout entier n,…”

Section: Introductionunclassified

Oscillations localisées sur les diviseurs

Bretèche¹,

Tenenbaum²

2012

Journal of the London Mathematical Society

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“…In particular, it was noted fairly early after the development of ZERODUR, an ultra-low CTE glass-ceramic manufactured by SCHOTT, that the He permeability was very low, some two orders of magnitude lower than fused silica [27], and as low as some glasses optimized for laboratory tubing that require exceptionally low gas permeation rates [28]. TEM images [29] support this view as well. TEM images [29] support this view as well.…”

Section: Detailed Nature Of the Interfacementioning

confidence: 99%

Practical aspects and implications of interfaces in glass-ceramics: a review

Davis¹

2008

International Journal of Materials Research

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Practical aspects and implications of interfaces in glass-ceramics: a reviewGlass-ceramics, prepared from the crystallization of interface-free, homogeneous glass, offer a unique perspective to study the influence of interfaces owing to the controlled manner in which interfaces (grain boundaries) can be introduced into the material. This review begins by considering the kinetics of interface development, itself strongly influenced by surface energetics. We then take up mechanical properties, the increase of which over that of their glassy precursors remains a cornerstone of what makes glass-ceramics desirable. Here, the role of the interface, both between crystals and, in some cases, within crystals (e. g., twin planes), serve to provide multiple ways in which to produce tough and strong materials. Hermetic crystal -glass interfaces are probably the rule in most glass-ceramics, rather than the exception, and are well demonstrated by several systems. Crystal clamping -the process by which crystals surrounded by residual glass in a glass-ceramic undergo stress due to coefficient of thermal expansion mismatches or by the inability of the crystal to go through a polymorphic transition upon cooling -has now been demonstrated in a number of studies with calculated stresses reaching 1 GPa. Electrical property studies of multi-phase glass-ceramics have shown the wide variety of phenomena possible with these materials, although more detailed studies will be necessary to fully understand the complex interplay between crystals, grain boundaries, space-charge regions, and residual glass. Light scattering is one of the more important implications of interfaces in glass-ceramics and quantitative approaches are more and more used to characterize this often unwanted feature. Concluding this review, we attempt to address four key questions that seek to extract those features of interfaces in glass-ceramics that have been application-enabling, require additional understanding and, finally, which might point a way towards new applications in the future.

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“…The function M(n, z) has been studied by various authors (see [4], [1], [6], [7], [5], [9], [3] for example). In [4] it is established that…”

Section: Introductionmentioning

confidence: 99%