A value-distribution criterion for the class $L~{\rm log} L$ and some related questions

M. Essen; D. F. Shea; C. S. Stanton

Displaying similar documents to “A value-distribution criterion for the class $L \log L$ and some related questions”

Sharp $L \log^{α} L$ inequalities for conjugate functions

Matts Essén, Daniel F. Shea, Charles S. Stanton (2002)

Annales de l’institut Fourier

Similarity:

We give a method for constructing functions $φ$ and $ψ$ for which $H (x, y) = φ (x) - ψ (y)$ has a specified subharmonic minorant $h (x, y)$ . By a theorem of B. Cole, this procedure establishes integral mean inequalities for conjugate functions. We apply this method to deduce sharp inequalities for conjugates of functions in the class $L {log}^{α} L$ , for $- 1 \leq α < \infty$ . In particular, the case $α = 1$ yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the conjugates of functions in $L log L$ . We also apply the method to produce a new...

An explicit formula for the Mahler measure of a family of $3$ -variable polynomials

Chris J. Smyth (2002)

Journal de théorie des nombres de Bordeaux

Similarity:

An explicit formula for the Mahler measure of the $3$ -variable Laurent polynomial $a + b x^{- 1} + c y + (a + b x + c y) z$ is given, in terms of dilogarithms and trilogarithms.

A note on the growth of entire functions.

Chung-Chung Yang (1975)

Collectanea Mathematica

Similarity:

A simple elementary proof of $M (x) = \sum_{n \leq x} μ (n) = o (x)$

M. Kalecki (1967)

Acta Arithmetica

Similarity:

Absolute values of BMOA functions.

Konstantin M. Dyakonov (1999)

Revista Matemática Iberoamericana

Similarity:

The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.

On the maximal order in $S_{n}$ and $S *_{n}$

M. Szalay (1980)

Acta Arithmetica

Similarity:

On ideals free of large prime factors

Eira J. Scourfield (2004)

Journal de Théorie des Nombres de Bordeaux

Similarity:

In 1989, E. Saias established an asymptotic formula for $Ψ (x, y) = |\{n \leq x : p ∣ n \Rightarrow p \leq y\}|$ with a very good error term, valid for $exp ({(log log x)}^{(5 / 3) + ϵ}) \leq y \leq x$ , $x \geq x_{0} (ϵ)$ , $ϵ > 0 .$ We extend this result to an algebraic number field $K$ by obtaining an asymptotic formula for the analogous function $Ψ_{K} (x, y)$ with the same error term and valid in the same region. Our main objective is to compare the formulae for $Ψ (x, y)$ and $Ψ_{K} (x, y),$ and in particular to compare the second term in the two expansions.

Some Estimates of the Integral $i n t_{0}^{2 p i} e x t L o g, | p (e^{i h e t a}) | {(2 p i)}^{- 1}, d h e t a$

Stojan Radenović (1992)

Publications de l'Institut Mathématique

Similarity:

Displaying similar documents to “A value-distribution criterion for the class L log L and some related questions”

Displaying similar documents to “A value-distribution criterion for the class $L \log L$ and some related questions”