Displaying similar documents to “Optimal bound for the discrepancies of lacunary sequences”

Diophantine approximation in Banach spaces

Lior Fishman, David Simmons, Mariusz Urbański (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.

Diophantine Approximations of Infinite Series and Products

Ondřej Kolouch, Lukáš Novotný (2016)

Communications in Mathematics

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This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos' results on~irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.

Diophantine Equations in Low Dimensions

Enrico Bombieri (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This lecture is a survey of recent results in the theory of diophantine equations, especially for dimension 1. The unit equation and its generalizations are examined in detail, as well as Baker's theory and the consequences of the abc-conjecture.