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On the distribution of consecutive square-free numbers of the form $vert alpha n vert cdots vert alpha n vert +1$

S. I. Dimitrov
장전수학회 (Jangjeon Mathematical Society)|2019.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제22권 제3호|pp. 463-470|DOI 10.17777/pjms.2019.22.3.010

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참고문헌

키워드

Consecutive square-free numbersAsymptotic formula
주제분류수학

초록

In the present paper we show that there exist infinitely many consecutive squarefree numbers of the form [ n], [ n] + 1, where > 1 is irrational number with bounded partial quotient or irrational algebraic number.

Abstract

In the present paper we show that there exist infinitely many consecutive squarefree numbers of the form [ n], [ n] + 1, where > 1 is irrational number with bounded partial quotient or irrational algebraic number.

참고문헌 (13)

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  6. A. M. Guloglu, "Sums of multiplicative functions over a Beatty sequence", Bull. Austral. Math. Soc., 78, pp.327~334 (2008)
  7. D. R. Heath-Brown, "The Square-Sieve and Consecutive Square-Free Numbers", Math. Ann, 266, pp.251~259 (1984)
  8. A. Karatsuba, "Principles of the Analytic Number Theory" (1983), Nauka
  9. L. Mirsky, "On the frequency of pairs of square-free numbers with a given difference", Bull. Amer. Math. Soc., 55, pp.936~939 (1949)
  10. "2014", ~
  11. J. D. Vaaler, "Some extremal problems in Fourier analysis", Bull. Amer. Math. Soc, 12, pp.183~216 (1985)
  12. R. C. Vaughan, "On the distribution of αp modulo 1", Mathematika, 24, pp.135~141 (1977)
  13. G. D. Victorovich, "On additive property of arithmetic functions", pp.2013

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