On log-subharmonicity of singular values of matrices

Bernard Aupetit

Displaying similar documents to “On log-subharmonicity of singular values of matrices”

On the fractional parts of $x / n$ and related sequences. II

Bahman Saffari, R. C. Vaughan (1977)

Annales de l'institut Fourier

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As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of $x h (x)$ where $h$ is an arithmetical function (namely $h (n) = 1 / n$ , $h (n) = log n$ , $h (n) = 1 / log n$ ) and $n$ is an integer (or a prime order) running over the interval $[y (x), x)]$ . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.

A “Hardy-Littlewood” approach to the $S$ -unit equation

G. R. Everest (1989)

Compositio Mathematica

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Linearization of analytic and non-analytic germs of diffeomorphisms of $(ℂ, 0)$

Timoteo Carletti, Stefano. Marmi (2000)

Bulletin de la Société Mathématique de France

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On the almost Goldbach problem of Linnik

Jianya Liu, Ming-Chit Liu, Tianze Wang (1999)

Journal de théorie des nombres de Bordeaux

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Under the Generalized Riemann Hypothesis, it is proved that for any $k \geq 200$ there is $N_{k} > 0$ depending on $k$ only such that every even integer $\geq N_{k}$ is a sum of two odd primes and $k$ powers of $2$ .

On Bloch functions and gap series.

Daniel Girela (1991)

Publicacions Matemàtiques

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Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general...

On an estimate of Walfisz and Saltykov for an error term related to the Euler function

Y.-F. S. Pétermann (1998)

Journal de théorie des nombres de Bordeaux

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The technique developed by A. Walfisz in order to prove (in 1962) the estimate $H (x) ≪ {(log x)}^{2 / 3} {(log log x)}^{4 / 3}$ for the error term $H (x) = \sum_{n \leq x} \frac{φ (n)}{n} - \frac{6}{π^{2}} x$ related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of $H (x) ≪ {(log x)}^{2 / 3} {(log log x)}^{1 + ϵ}$ is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical -...

A simple proof of the mean fourth power estimate for $ζ (\frac{1}{2} + i t)$ and $L (\frac{1}{2} + i t, χ)$

K. Ramachandra (1974)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Dirichlet series of $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : On an error term associated with its coefficients

U. Balakrishnan, Y.-F. S. Pétermann (1996)

Acta Arithmetica

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