Errata to the paper “A new estimate for the sum $M(x)=\sum _{n≤x} μ(n)$” (Acta Arithmetica 13(1967), pp. 49-59)

R. MacLeod

Displaying similar documents to “Errata to the paper “A new estimate for the sum $M (x) = \sum_{n \leq x} μ (n)$ ” (Acta Arithmetica 13(1967), pp. 49-59)”

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Andrzej Schinzel (1969)

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Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster (2002)

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We consider a Cauchy problem $y^{'} (x) + y^{2} (x) = q (x), {y (x)|}_{x = x_{0}} = y_{0}$ where $x_{0}$ , $y_{0} \in R$ and $q (x) \in L_{1}^{loc} (R)$ is a non-negative function satisfying the condition: $\int_{- \infty}^{x} q (t) d t > 0, \int_{x}^{\infty} q (t) d t > 0 for x \in R .$ We obtain the conditions under which $y (x)$ can be continued to all of $R$ . This depends on $x_{0}$ , $y_{0}$ and the properties of $q (x)$ .

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Cramér's formula for Heisenberg manifolds

Mahta Khosravi, John A. Toth (2005)

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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 the product of the conjugates outside the unit circle of an algebraic integer

A. Bazylewicz (1976)

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On Ramanujan's continued fraction

K. Ramanathan (1984)

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Displaying similar documents to “Errata to the paper “A new estimate for the sum M ( x ) = ∑ n ≤ x μ ( n ) ” (Acta Arithmetica 13(1967), pp. 49-59)”

Corrigendum to the papers "On two theorems of Gelfond and some of their applications" and "On primitive prime factors of Lehmer numbers III"

Classification of initial data for the Riccati equation

On equations with reflection

Cramér's formula for Heisenberg manifolds

On the product of the conjugates outside the unit circle of an algebraic integer

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Addendum to the paper "On the product of the conjugates outside the unit circle of an algebraic number"

Displaying similar documents to “Errata to the paper “A new estimate for the sum $M (x) = \sum_{n \leq x} μ (n)$ ” (Acta Arithmetica 13(1967), pp. 49-59)”