On the theorem of Jarník and Besicovitch
R. Kaufman (1981)
Acta Arithmetica
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R. Kaufman (1981)
Acta Arithmetica
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Matts Essén, Daniel F. Shea, Charles S. Stanton (2002)
Annales de l’institut Fourier
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We give a method for constructing functions and for which has a specified subharmonic minorant . 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 , for . In particular, the case yields an improvement of Pichorides’ form of Zygmund’s classical inequality for the conjugates of functions in . We also apply the method to produce a new...
M. Essen, D. F. Shea, C. S. Stanton (1985)
Annales de l'institut Fourier
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We give a necessary and sufficient condition for an analytic function in to have real part in class . This condition contains the classical one of Zygmund; other variants are also given.
Fernando Soria (1985)
Studia Mathematica
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Antanas Laurinčikas (1996)
Journal de théorie des nombres de Bordeaux
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A limit theorem in the space of continuous functions for the Dirichlet polynomial where denote the coefficients of the Dirichlet series expansion of the function in the half-plane , and , 1n and as , is proved.
Chris J. Smyth (2002)
Journal de théorie des nombres de Bordeaux
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An explicit formula for the Mahler measure of the -variable Laurent polynomial is given, in terms of dilogarithms and trilogarithms.
P. K. Jain, D. R. Jain (1974)
Annales de l'institut Fourier
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The estimations of lower order in terms of the sequences and for an entire Dirichlet series , have been obtained, namely : One of these estimations improves considerably the estimations earlier obtained by Rahman (Quart. J. Math. Oxford, (2), 7, 96-99 (1956)) and Juneja and Singh (Math. Ann., 184(1969), 25-29 ).
Curtis D. Bennett, Josef Blass, A. M. W. Glass, David B. Meronk, Ray P. Steiner (1997)
Journal de théorie des nombres de Bordeaux
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In this paper we prove a lower bound for the linear dependence of three positive rational numbers under certain weak linear independence conditions on the coefficients of the linear forms. Let with positive integers and positive multiplicatively independent rational numbers greater than . Let with coprime positive integers . Let and assume that gcd Let and assume that We prove that either is -linearly dependent over (with respect to )...