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- W2080456895 abstract "In this paper, together with [7] and [8], we shall be concerned with estimating the number of solutions of the inequality for almost all α (in the sense of Lebesgue measure on Iℝ), where , and both m and n are restricted to sets of number-theoretic interest. Our aim is to prove results analogous to the following theorem (an improvement given in [2] of an earlier result of Khintchine [10]) and its quantitative developments (for example, see [11, 12,6]): Let ψ(n) be a non-increasing positive function of a positive integer variable n. Then the inequality (1·1) has infinitely many, or only finitely many, solutions in integers to, n(n > 0) for almost all real α, according to whether the sum diverges, or converges, respectively." @default.
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- W2080456895 date "1988-03-01" @default.
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- W2080456895 title "Metric Diophantine approximation with two restricted variables I. Two square-free integers, or integers in arithmetic progressions" @default.
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- W2080456895 doi "https://doi.org/10.1017/s030500410006477x" @default.
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