Balls defined by nonsmooth vector fields and the Poincaré inequality

Annamaria Montanari; Daniele Morbidelli

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The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1

Jerzy Sawa (1985)

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H. König, D. Lewis, P.-K. Lin (1983)

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Periodically forced damped beams resting on nonlinear elastic bearings

Michal Fečkan (2005)

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Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

Annales de l'institut Fourier

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Let $R (λ)$ be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that $\int_{1}^{T} {| R (t) |}^{2} d t = c T^{\frac{5}{2}} + O_{δ} (T^{\frac{9}{4} + δ})$ , where $c$ is a specific nonzero constant and $δ$ is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that $R (t) = O_{δ} (t^{\frac{3}{4} + δ})$ .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the $2 n + 1$ -dimensional case. ...

On Ramanujan's continued fraction

K. Ramanathan (1984)

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